The extent of the atonment
Critics seem to object that the atonement is applicable to all who have ever lived. They want to restrict it to only those who lived after the Savior ("only after Christ's death" and "for the believer").
This doesn't only limit its accessibility to those who lived before the Savior, it quite literally slams the door on the possibility of their ever receiving salvation. The Gospel of Jesus Christ does not restrict itself in that manner. All will be raised from the dead; all will stand before God to be judged; all will be expected to give an accounting of their behavior on Earth. And they will all be held to basically the same standard. No one slides into heaven, or gets there by hanging onto the tailcoats of another. No one is saved on borrowed light.
The Council of Quiersy, convened in 853, in a passage quoted by evangelical scholar Thomas Oden, declared that "as there never was, is or will be any man whose nature was not assumed by our Lord Jesus Christ, so there never was, is or will be any man for whom He has not suffered; though not all are redeemed by the mystery of His passion."  How is it that Christ suffered for all, but did not redeem all? Either Christ's passion was not universal, or "redemption" has a specialized meaning. Clearly all those whose nature has been assumed, which is to say, all who have ever been born, will receive the benefits of His death and resurrection; but also clearly, not all are going to be redeemed because not all have chosen to follow. The paragraph, in the part not quoted by Thomas Oden, refers to those who are "unfaithful," and "those not believing in faith those things 'which He has worked through love' [Galatians 5:6]," that is, those who do not believe in what Christ did for them, which "has indeed in itself that it may be beneficial to all; but if it is not drunk, it does not heal." If we do not drink the cup the Savior offers us, the atonement will not heal us.
The extent to which the atonement is applicable has been a hotly debated topic in Christian history, in all traditions, but none more so than in evangelical circles. A recently published book presents several dissenting voices to the position taken by critics, that is, that only those who believe are affected by the atoning sacrifice of the Savior. I. Howard Marshall says that:
The question at issue is not whether all will be saved but whether God has made provision in Christ for the salvation of all, provided that they believe, and without limiting the potential scope of the death of Christ merely to those whom God knows will believe. 
Marshall, Professor of New Testament exegesis at University of Aberdeen, in Scotland, is one of the leading evangelical scholars today. He concludes his study of the Pastoral epistles by writing that "we have found nothing in the Pastorals that requires that we assume the existence of a 'hidden agenda,' a secret plan of God to save only the elect."  He refers to some passages in Romans 8–11 and in Ephesians 1 that are frequently taken to refer to the elect having been pre-destined to that status. While not discussing these verses in detail, he does state, "I do not find grounds in these passages for the view that God has purposed to save only a limited number of the elect." 
Terry L. Miethe is a Baptist; he is the Dean of the Oxford Study Center at Oxford, England. He is also the Managing Editor of Moody Press. The purpose of a paper he wrote is to defend the thesis that "the redemptive events in the life of Jesus provided a salvation so extensive and so broad as to potentially include the whole of humanity past, present, and future!"  The position Miethe is defending is called unlimited atonement.
"The idea that the death of Christ was designed to include all humankind but is applied only to those who accept it, believe in Jesus as Lord and Savior, is referred to as the "unlimited" or "general" atonement. There are many passages in the Bible that clearly teach this idea. 
Miethe refers to Isaiah 53:6; Matthew 11:28; John 3:16–17; 1 Timothy 2:6, 4:10; Titus 2:11, Hebrews 2:9; 2 Peter 3:9; 1 John 2:2; and Revelation 22:17. He also states that the following have been professors of the unlimited atonement view: Clement of Alexandria (d. 220), Eusebius (d. 340); Athanasius (373), Cyril of Jerusalem (386), Gregory Nazianzen (d. 389); Basil (379), Ambrose (407), Cyril of Alexandria (d. 444), Richard Hooker (d. 1600), James Ussher (d. 1656), Richard Baxter (d. 1691), John Bunyan (d. 1688), John Newton (d. 1807), Alfred Edersheim (b. 1825), B.F. Westcott (d. 1901), J.B. Lightfoot (b. 1828), Augustus H. Strong (d. 1921), A.T. Robertson (b. 1863), and "many others."  There are some important scriptures and some important scholars in those two lists. All of them would apparently take exception to the position critics uphold.
On 1 Timothy 2:1 Miethe quotes F.F. Bruce: "To say that He died for His people is certainly Scriptural…but it is equally Scriptural to say that He died for all… And when Scripture says 'all' in a context like this, it means 'all.'" Bruce also quotes John Calvin on the universality of the blood that was "shed for many;" Calvin wrote that "by the word many he means not a part of the world only but the whole human race."  In discussing 1 Timothy 4:10 ("who is the Savior of all men, and especially those who believe"), Miethe quotes evangelical scholar Millard Erickson who wrote: "This is a particularly interesting and significant verse, since it brackets as being saved by God both believers and others, but indicates that a greater degree of salvation attaches to the former group.'"  This corresponds precisely to the LDS position; if critics want to state that it also agrees with their position, by virtue of having been written by a prominent evangelical scholar, then they will have to admit that their position is the same as the LDS! Miethe quotes from another evangelical, Robert H. Culpepper:
The Bible teaches that Christ died for 'sinners' (Rom 5.6-8; I Tim 1.15). The word 'sinner' nowhere means 'church' or 'the elect,' but simply all of lost mankind… Are we to suppose that the elect are the only ones who labor and are heavy laden and that they are thus the only ones to whom the invitation of Jesus is issued (Matt 11.28) or that the elect are the only ones who are invited to take the water of life without price (Rev 22.17)? Do not these invitations [made to all sinners] presuppose that the free response of man, though not meriting salvation, is nevertheless the condition upon which the benefits of the atonement are dispensed? Moreover, there are clear assertions in Scripture that Christ died for all (II Cor 5.14), that he gave himself a ransom for all (I Tim 2.6), that he is the expiation of the sins of the whole world (I John 2.2; cf. also I Tim 4.10; Titus 2.11), and that he tasted death for every man (Heb 2.9)." 
Notice again the reference to the "free response of man;" we must cooperate in our salvation, at least to the extent of accepting the atonement into our own lives.
It is Terry Miethe's contention that John Calvin was also a believer in 'unlimited atonement.' Miethe quotes the following from Calvin's works
- On Romans 5:18: "Christ suffered for the sins of the whole world."
- On John 1:29 Calvin wrote: "And when he says the sin of the world, he extends this favor indiscriminately to the whole human race."
- On Galatians 5:12 he writes: "it is the will of God that we should seek the salvation of all men without exception, as Christ suffered for the sins of the whole world."
In his Institutes of the Christian Religion Calvin wrote: "the way of salvation was not shut against any order of men; that, on the contrary, he had manifested his mercy in such a way, that he would have none debarred from it." 
Miethe's conclusion is clearly applicable to the position taken by critics:
The doctrine of limited atonement is logically contradictory to the clear teaching of passage after passage of Scripture… Second, it is theologically repugnant, for it misunderstands the nature of God and of man. The divine sovereignty of God and human freedom are analogical aspects of the relationship of God to man—of the Creator to that which was created in his image. Third, it is philosophically deficient, for the very existence of reason, or the ability to know, shows that man is capable of choice. Some doctrine of human freedom is essential to any meaningful theory of human responsibility. 
- [note] Partially quoted in Oden, The Word of Life, Vol. 2, 383. Entire paragraph is given at Henry Denzinger, Sources of Catholic Dogma, translated by Roy J. Deferrari from the 30th edition of Denzinger's Enchiridion Symbolorum (Fitzwilliam, New Hampshire: Loreto Publications, 2002), paragraph 319.
- [note] I. Howard Marshall, "Universal Grace and Atonement in the Pastoral Epistles," The Grace of God and the Will of Man, edited by Clark Pinnock (Minneapolis, Minnesota: Bethany House Publishers, 1989), 56.
- [note] Marshall, "Universal Grace and Atonement in the Pastoral Epistles," 69.
- [note] Marshall, "Universal Grace and Atonement in the Pastoral Epistles,"68–69.
- [note] Miethe, "The Universal Power of the Atonement," 72. Miethe's thesis is actually a quotation from Donald M. Lake, "He died for all: the Universal Dimensions of the Atonement," in Grace Unlimited, edited by Clark H. Pinnock (Minneapolis, Minnesota: Bethany House Publishers, 1975), 31.
- [note] Miethe, "The Universal Power of the Atonement," 78–79, emphasis in the original.
- [note] Ibid., 79. In the footnote Miethe refers to Norman F. Douty, The Death of Christ: Did Christ Die Only for the Elect? (Irving, Texas: William and Watrous, 1978), 136–163, who lists "over 70 of the Church's leading teachers—from the early centuries to the present one." Miethe also states that John Calvin himself must have been a believer in unlimited atonement, page 85–86. Alan Clifford concurs, Atonement and Justification, 72–73: "there is considerable evidence to suggest that, judged by seventeenth-century criteria, he did not subscribe to, nor believe in, the doctrine of limited atonement." On page 73 Clifford quotes Calvin: "God commends to us the salvation of all men without exception, even as Christ suffered for the sins of the whole world" (Comm Galatians 5:12). See in general the entire treatment by Clifford, in Part Two: The Theology. Atonement and Grace: Chapter Five: Authentic Calvinism, pages 69–94.
- [note] Miethe, "The Universal Power of the Atonement," 80, quoting Frederick F. Bruce, Answers to Questions (Grand Rapids, Michigan: Zondervan, 1972), 197. No source is given for the Calvin comment, but it is probably from Calvin's Commentary on a Harmony of the Evangelists, three volumes, translated by William Pringle (Grand Rapids, Michigan: Baker Books, 1979), in volume 3, on Matthew 26:28 and Mark 14:24.
- [note] Miethe, "The Universal Power of the Atonement," 80, quoting Millard J. Erickson, Christian Theology, Vol. 2 (Grand Rapids, Michigan: Baker Books, 1984), 830.
- [note] Ibid., 82, quoting Culpepper, Interpreting the Atonement (Grand Rapids, Michigan: Eerdmans, 1966), 125.
- [note] Ibid., 88–90. The quotation is from the Institutes 3.24.6. Miethe also refers us to the following passages: Institutes of the Christian Religion 3.1.1; 3.24.17; Eternal Predestination of God 9.5, and commentaries on Isaiah 53.12; Romans 5.15; Colossians 1.15.
- [note] Ibid., 92.