Calvinists and Arminians disagree over the scope of Jesus' atoning work. Calvinists argue that the saving work of Jesus is intended exclusively for the elect. God has chosen the unchangeable number of those to be saved, and Christ's work is effective for them alone. Arminians see this as a denial of the clear teaching of scripture that the scope of Christ's atoning work is unlimited being sufficient for the salvation of every person and applied to a person on the condition of faith in Christ.
One of the key texts for the Arminian understanding of unlimited atonement is Romans 5:15, 18-19 where Paul says, "But the free gift is not like the trespass. For if the many died through the one man's trespass, much more surely have the grace of God and the free gift in the grace of the one man, Jesus Christ, abounded for the many...Therefore just as one man's trespass led to condemnation for all, so one man's act of righteousness leads to justification and life for all. For just as by the one man's disobedience the many were made sinners, so by the one man's obedience the many will be made righteous."
For Paul, if we are to understand the nature of Christ's atoning work for us, we need to understand the nature of Adam's transgression. The sin of the one man, Adam, led to death for all. In Adam, all sinned and died. In his sin, Adam represented the entire human race and the entire human race fell as a consequence. Paul's term for the entire human race here is "the many." Calvinists and Arminians agree that the extent of the fall was unlimited with regard to the whole human race.
Paul draws out the similarity between the transgression of Adam and the obedience of Christ through his use of the term "the many." In Adam, the many were made sinners. Likewise, in Christ, grace abounds to the many. That means that the scope of the atonement is equal to the scope of Adam's transgression. The work of Christ abounds to all those who, in Adam, sinned and died. If Adam's transgression caused the entire human race to fall, then the provision of Christ's atoning work is extended to the entire human race as well.
Now if there is similarity between Adam and Christ, there is also a difference. In Adam, all died without condition. However, in Christ, the benefits of his saving work are applied on the condition of faith, as Paul has indicated earlier in the letter (cf. 3:21-26). This is what guards us against using this text to teach universal salvation.
It should be clear, then, that the provision for salvation in Christ extends as far as the penalty of Adam's transgression. That is, the atoning work of Christ is unlimited in its scope.