One of the most explicit evidences of the doctrine of universal salvation in the bible is found in Paul's letter to the Romans, more specifically 5.18-9:
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.
It is clear that Paul's use of "the many" through the section spanning 5:12-21 is not intended to be understood exclusively, as if it meant "many but not all." The Greek phrase is οἱ πολλοί, hoi polloi, which we all know is a general way of referring to the masses of humanity. More specifically Paul intends to underscore the contrast between the actions of a single person ("the one") and their consequences for the rest of humanity ("the many"). Paul's language in these two particular verses, moreover, seems plainly to affirm that the universal deleterious effects of Adam's sin will be undone by a universally salutary act of obedience by Christ; hence universal salvation.
Now in research for a paper I will be writing for my New Testament Exegesis course, I came across a recent commentary on the letter to the Romans written by Colin G. Kruse (2012). In commenting upon this text he says:
Paul statement that ‘just as one trespass resulted in condemnation for all people, so also one righteous act resulted in justification and life for all people’ would appear on first reading to imply that just as Adam’s trespass affected all people without exception, so also Christ’s righteous act likewise affects all people without exception, and in fact there are those who argue that this is what Paul intends.76 But this would be a misreading of the apostle, for already he has said that it is ‘those who receive God’s abundant provision of grace and of the gift of righteousness’ who will ‘reign in life’ (5:17, italics added). The ‘all people’ of the latter part of the phrase is best understood to mean all who receive the gift of grace, whether they are Jews or Gentiles (Kruse, Paul's Letter to the Romans, p. 251).
Kruse's escape, then, is that Paul implicitly qualifies his universal statements with the use of the word "receive" (λαμβάνοντες). Because this grace must be 'received,' consequently he does not mean that literally all persons will be saved.
This is a very weak counterargument, however, for which there are a number of compelling responses. In the first place, we may simply infer in the other direction that Paul means to imply that all persons will eventually receive this grace, rather than that some persons not receiving will not be transformed. On the other hand, I would also argue that this involves a misinterpretation of the word λαμβάνω as Paul uses it here. He is referring not to accepting but to receiving, to being given salvation rather than to taking a salvation offered.
Paul's emphasis here is on the passivity of humanity in the process of salvation. In the apostle's understanding, humanity -- while retaining a responsibility and culpability for its own sins -- is in an important way a victim of the mistake of Adam, the first man. His sin brought condemnation and death for the rest of them who came after him. In this condition of sin and death humanity can hardly be considered capable of accepting a salvation offered to it, especially one which contradicts the very tendencies typical of humanity's sinfulness. Humanity receives a deliverance that comes from without it, and it must be this way because of its incapacitated position. Paul speaks of humanity receiving because it is passive in this exchange.
Now precisely because humanity is in part a victim, even granting the responsibility it has for its own sins, it does not make sense to make autonomous acceptance of grace a condition of salvation. The condition from which this "autonomous" choice must be made is a sinful, fallen, corrupted one; that makes the choice in itself anomalous and an extreme rarity, if not an impossibility. Yet it would make no sense of Paul's earlier repeated phrase, "how much more", if not all those who inherit Adam's cursed condition are subsequently saved by Christ. Grace will not have abounded "that much more" unto life and justification and the rest if there remain some outside the domain of grace's effective saving operation.