There is much room for agreement on atonement… and misunderstandings to avoid on all sides. Libertarians (both Traditionalists and Arminians) can find unexpected common ground even with a Reformed theologian, such as Charles Hodge:
The righteousness of Christ being of infinite value or merit, and being in its nature precisely what all men need, may be offered to all men. It is thus offered to the elect and to the non-elect; and it is offered to both classes conditionally. That condition is a cordial acceptance of it as the only ground of justification. If any of the elect (being adults) fail thus to accept of it, they perish. If any of the non-elect should believe, they would be saved. What more does any Anti-Augustinian scheme provide? The advocates of such schemes say, that the design of the work of Christ was to render the salvation of all men possible. All they can mean by this is, that if any man (elect or non-elect) believes, he shall, on the ground of what Christ has done, be certainly saved. But Augustinians say the same thing. Their doctrine provides for this universal offer of salvation, as well as any other scheme. It teaches that God in effecting the salvation of his own people, did whatever was necessary for the salvation of all men, and therefore to all the offer may be, and in fact is made in the gospel. If a ship containing the wife and children of a man standing on the shore is wrecked, he may seize a boat and hasten to their rescue. His motive is love to his family; his purpose is to save them. But the boat which he has provided may be large enough to receive the whole of the ship’s company. Would there be any inconsistency in his offering them the opportunity to escape? Or, would this offer prove that he had no special love to his own family and no special design to secure their safety? And if any or all of those to whom the offer was made, should refuse to accept it, some from one reason, some from another; some because they did not duly appreciate their danger; some because they thought they could save themselves; and some from enmity to the man from whom the offer came, their guilt and folly would be just as great as though the man had no special regard to his own family, and no special purpose to effect their deliverance… This is precisely what God, according to the Augustinian doctrine, has actually done. Out of special love to his people, and with the design of securing their salvation, He has sent his Son to do what justifies the offer of salvation to all who choose to accept of it. Christ, therefore, did not die equally for all men. He laid down his life for his sheep; He gave Himself for his Church. But in perfect consistency with all this, He did all that was necessary, so far as a satisfaction to justice is concerned, all that is required for the salvation of all men. So that all Augustinians can join with the Synod of Dort in saying, “No man perishes for want of an atonement.”
The Libertarian may at first be put off by the idea of God sacrificing His Son out of a special love for the elect. But if it is kept in mind that the special love that God has had for the Church even from eternity past is what is in view in such language; and that God, knowing who would believe and be part of that Bride of Christ, intended first and foremost for Christ’s sacrifice to be a purchase in blood for the purpose of saving that particular people, then it can be concluded that such a wonderful sacrifice was intended for those who would believe in a way in which it was not intended for those who would never believe. The purpose of providing a universally applicable sacrifice that may be rejected or accepted is secondary to the purpose of redeeming those who will actually believe.
Andrew Fuller offers an excellent centrist perspective that ties this together:
Were I asked concerning the gospel, when it is introduced into a country, For whom was it sent? if I had respect only to the revealed will of God, I should answer, It is sent for men, not as elect or non-elect, but as sinners. It is written and preached “that they might believe that Jesus is the Christ, the Son of God, and that believing they might have life through his name.” But if I had respect to the appointment of God, with regard to its application, I should say, If the Divine conduct in this instance accord with what it has been in other instances, he hath visited that country, to “take out of it a people for his name.” In like manner, concerning the death of Christ, if I speak of it irrespective of the purpose of the Father and the Son as to the objects who should be saved by it, referring merely to what it is in itself sufficient for, and declared in the gospel to be adapted to, I should think I answered the question in a Scriptural way in saying, It was for sinners as sinners. But if I have respect to the purpose of the Father in giving his Son to die, and to the design of Christ in laying down his life, I should answer, It was for his elect only.
William Shedd, another Reformed theologian, expands on the different meanings of “for,” and the potential for agreement:
The dispute also turns upon the meaning of the preposition for. One theologian asserts that Christ died “for” all men, and another denies that Christ died “for” all men. There may be a difference between the two that is reconcilable, and there may be an irreconcilable difference. The preposition for denotes an intention of some kind. If, in the case under consideration, the intention is understood to be the purpose on the part of God both to offer and apply the atonement by working faith and repentance in the sinner’s heart, by the operation of the Holy Spirit, then he who affirms that Christ died “for” all men is in error, and he who denies that Christ died “for” all men holds the truth. These two parties are irreconcilable.
But he who asserts that Christ died “for” all men may understand the intention signified by the preposition to be the purpose on the part of God only to offer the atonement, leaving it to the sinner whether it shall be appropriated through faith and repentance. The intention, in this latter case, does not include so much as in the former, and the preposition is narrower in meaning. When the word for is thus defined, the difference between the two parties is reconcilable. The latter means by for “intended for application.”
Again, the preposition for is sometimes understood to denote not intention, but value or sufficiency. To say that Christ died “for” all men then means that his death is sufficient to expiate the guilt of all men. Here, again, the difference is possibly reconcilable between the parties. The one who denies that Christ died “for” all men takes “for” in the sense of intention to effectually apply. The other who affirms that Christ died “for” all men takes “for” in the sense of value…
Shedd’s solution is that atonement speaks of sufficiency, while redemption speaks of application:
The distinction between the “sufficiency” of the atonement and its “extent” in the sense of “intent” or effectual application is an old and well-established one. It is concisely expressed in the dictum that Christ died “sufficiently for all, but efficiently only for the elect”…
Atonement must be distinguished from redemption. The latter term includes the application of the atonement… Since redemption includes reconciliation with God and inheritance in the kingdom of heaven, it implies something subjective in the soul: an appropriation by faith of the benefits of Christ’s objective work of atonement…
Atonement is unlimited, and redemption is limited. This statement includes all the scriptural texts: those which assert that Christ died for all men, and those which assert that he died for his people. He who asserts unlimited atonement and limited redemption cannot well be misconceived. He is understood to hold that the sacrifice of Christ is unlimited in its value, sufficiency, and publication, but limited in its effectual application.
The fact that Christ’s death is sufficient to pay for the sins of any man, and is universally applicable, does nothing to extinguish the debt of those who have not put their faith in Him. Shedd explains:
The mere fact that Jesus Christ made satisfaction for human sin, alone and of itself, will save no soul. Christ, conceivably, might have died precisely as he did and his death have been just as valuable for expiatory purposes as it is, but if his death had not been followed with the work of the Holy Spirit and the act of faith on the part of individual men, he would have died in vain. Unless his objective work is subjectively appropriated, it is useless so far as personal salvation is concerned…
The supposition that the objective satisfaction of justice by Christ saves of and by itself, without any application of it by the Holy Spirit and without any trust in it by the individual man, overlooks the fact that while sin has a resemblance to a pecuniary debt, as is taught in the petition “forgive us our debts,” it differs from it in two important particulars. In the instance of pecuniary indebtedness, there is no need of a consent and arrangement on the part of the creditor when there is a vicarious payment. Any person may step up and discharge a money obligation for a debtor, and the obligation ceases ipso facto. But in the instance of moral indebtedness to justice or guilt, there must be a consent of the creditor, namely, the judge, before there can be a substitution of payment… Second, after the vicarious atonement has been permitted and provided, there is still another condition in the case, namely, that the sinner shall confess and repent of the sin for which the atonement was made and trust in the atonement itself…
Fuller also emphasizes the misunderstandings that come from taking the metaphor of payment of debt to an unwarranted extreme:
I apprehend, then, that many important mistakes have arisen from considering the interposition of Christ under the notion of paying a debt. The blood of Christ is indeed the price of our redemption, or that for the sake of which we are delivered from the curse of the law; but this metaphorical language, as well as that of head and members, may be carried too far, and may lead us into many errors… Sin is a debt only in a metaphorical sense; properly speaking, it is a crime, and satisfaction for it requires to be made, not on pecuniary, but on moral principles…
The reason for this difference is easily perceived. Debts are transferable, but crimes are not…
The ramifications are clear. Since atonement does not proceed on the order of the payment of a debt, then no sinners have the benefits of Christ’s death applied to them unless and until they come to Christ in faith (which the Judge in the case requires). But even then, it is a one-for-one substitution. Because the sinner’s debt is criminal, each individual sinner owes the entirety of Christ’s suffering and death. Most Baptists see Christ’s sacrifice as an overabundance, paying for the sins of all God intends for it to pay, and with an infinite surplus of “value.” As Millard Erickson sees it, the reason that Christ’s sacrifice is able to save so many is because it is of infinite value:
When evangelicals ask the question, “For whom did Christ die?” they are not asking whether the death of Christ has value sufficient to cover the sins of all persons. There is total agreement on this matter. Since the death of Christ was of infinite value, it is sufficient regardless of the number of elect…
But this is flawed, as it makes each sinner’s share of those three hours of vicarious suffering infinitely small, so that only an infinitely small part of Christ’s suffering was necessary to pay what I owed for my sin. Not only is sin devalued, it is infinitely devalued. The Cross does not save on the principle of a value-based transaction, but on the principle of one-for-one substitution. As Fuller rightly points out, if the same sacrifice is required to save one sinner as to save all sinners, then there is no more “propriety” in asking, “Whose sins were laid on Christ?” Atonement must proceed on the principle of one-for-one substitution alone.
But notice the further restriction, mentioned by Fuller: “Debts are transferable, but crimes are not.” Gordon Clark calls this “a major problem:”
The distinction is this: If Mr. X owes Mr. Y a hundred dollars, financial justice is completely satisfied if Mr. Z pays the debt for Mr. X. But if Mr. X robs a bank or murders someone, Mr. Z cannot satisfy justice by taking his punishment. Criminal justice requires that the criminal himself, and no one else, must suffer the penalty. Now, since sin is a crime, not a financial debt, the satisfaction of divine justice without the penalty being imposed on the sinner himself constitutes a major problem.
This “intensely personal nature of guilt” is also acknowledged by Leon Morris:
An objection to this view arises from the intensely personal nature of guilt. My misdeeds are my own, and all the verbal juggling in the world cannot make them belong to someone else…
…If atonement consists simply in ignoring this, and putting the punishment arising from my yesterdays upon someone else, then a grave wrong has been done. Sin is not to be regarded as a detachable entity which may be removed from the sinner, parcelled up, and given to someone else. Sin is a personal affair. My guilt is my own.
Christ must do more than die in my place. God must find a way that Christ’s death and righteous life can be made mine just as if I had done them. Dr. Shedd tells us, “When a particular person trusts in this infinite atonement and it is imputed to him by God, it then becomes his atonement for judicial purposes as really as if he had made it himself, and then it naturally and necessarily cancels his personal guilt…” How then does God make Christ’s atonement to become mine as really as if I had made it myself? The answer is found in the spiritual union of Christ and the believer.
In and of itself, the shedding of the blood of the Sacrifice does nothing to satisfy the claims of justice upon the individual sinner. There must be a connection established between the Sacrifice and the sinner if the former is to affect the latter. While sovereignty is free from the exigencies of substantial reality, justice has no such license. God may sovereignly declare that a mere nominal connection between the Sacrifice and sinner is sufficient to free him from wrath, but He cannot justly do so. There are two ways in which justice must be satisfied: 1) justice must be satisfied that the penalty has been fully suffered within substantial reality; and 2) justice must be satisfied that the Sacrifice and sinner are so joined as to become one within substantial reality. Neither of these two can be mere choices within God’s mind to view them as if they were true (in contradiction to substantial reality). Justice demands more than that the sin be punished — justice demands that the one who sinned be punished.
The union of believers with Christ is spiritual, and not merely legal or “federal.” This union happens within the believer, and does not exist only within the mind of God. Rom. 6:3, “Or do you not know that as many of us as were baptized into Christ Jesus were baptized into His death?” and, 1 Cor. 6:17, “But he who is joined to the Lord is one spirit with Him.” It is not speaking of water baptism, but baptism into the Spirit, which happens at the point of saving faith. To be spiritually baptized into Christ is to be joined to Him so that the new believer and Christ are one spirit, and the result of this is that the new believer is joined to (or, baptized into) His death.
A man’s spirit is the core of his identity. When the Holy Spirit indwells the man, He creates a new man by joining the spirit of the man to the Spirit of Christ. They are not joined to the extent that either is lost in the other, but they are joined to the extent that the man’s new identity is in Christ and his old identity is no longer valid in the eyes of justice. In fact, the believer is so identified with Christ that he is considered to have been crucified with Him. Gal. 2:20, “I have been crucified with Christ; it is no longer I who live, but Christ lives in me, and the life which I now live in the flesh I live by faith in the Son of God, who loved me and gave Himself for me.” To be immersed into the Spirit of Christ is to be plunged into that flood of sufficiency that all His human experiences provide. For me to be saved requires more than that God see Christ on the cross: God must see the Christ of the cross in me. Only by the two becoming one can I gain a title to Christ’s righteous life and atoning sacrifice just as if they were mine. And God has required faith before He will give that saving union to the sinner. The applicability of the cross of Christ is universal in scope, but only those who put faith in Him have their sins atoned for by His sacrificial death.
Ken Hamrick, 2013
 Charles Hodge, Systematic Theology, (Peabody: Hendrickson, 2003), Vol. II, pp. 555-557
 Andrew Fuller, “Conversations Between Peter, James, and John,” The Complete Works of Andrew Fuller, (Harrisonburg: Sprinkle, 1988), Vol. II, pp. 689-690
 William G. T. Shedd, Dogmatic Theology, (Phillipsburg: P & R, 2003), Third ed., p. 741
 Ibid., pp. 742-743
 Ibid., pp. 726-727
 Fuller, “Conversations,” p. 688
 Millard Erickson, Christian Theology, (Grand Rapids: Baker, 1990), pp. 825-826
 Gordon Clark, The Atonement, (Jefferson: Trinity Foundaton, 1987), pp. 84-85
 Leon Morris, The Cross in the New Testament, (Eugene, OR: Wipf and Stock, 2006), p. 415
 Shedd, p. 725