Aside from the relatively few Biblical passages that are understood by those of the more “mainstream” evangelical Christian community (among whom I would count you, BA 
) as providing positive evidence that some will never be saved, it would seem that one of the greatest obstacles to their considering UR as a possibility is the glaring absence of any verses or passages that teach or give examples of post-mortem repentance and faith. Of course, a common response from Biblical universalists is that all of the passages that appear to teach (and which, for the most part, I would agree do teach) universal reconciliation simply presuppose that all necessary conditions of salvation - i.e., repentance and faith - will ultimately be met by everyone. Thus, by implication, these passages would, in fact, teach post-mortem repentance and faith. However, what I think has not been seriously considered as a possibility is the idea that our salvation from sin and relational alienation from God may not always be conditioned on our faith and repentance.
Now, I grant that for those who think it impossible or unlikely that God could (or would) save anyone apart from their conscious choice to be saved, the idea that faith and repentance may not always be necessary for salvation is going to be hard to swallow. But consider the following: if faith is only possible in a context of some ambiguity and uncertainty, when certain aspects of reality yet remain “unseen” and certain hopes remain unrealized (Heb 11:1), then wouldn’t it follow that, when the ambiguity and uncertainty is removed and the hope is realized, faith would be both unnecessary and impossible? Paul seems to suggest that “faith” is only necessary for us prior to that time when mortality is “swallowed up by life” and we will be “with the Lord” (2 Cor 5:4-8). If so, then is it possible that faith might not be necessary for anyone’s salvation at this time? In other words, is it possible that some may never be saved by faith because they will be instantly granted “sight?” If this were the case, then the “knowledge of the truth” (1 Tim 2:4) could be made known to them in such an immediate and overwhelming way that it would be impossible for them to resist or suppress it. And assuming that God is able to raise us from death with bodies and brains that are no longer subject to the temptations which serve as the occasions for sin in this life, then this fact, in conjunction with the instant “sight” which will be received, would mean that those raised from the dead will be sinless in nature, and thus subjected to Christ and subjects of the kingdom of God (1 Cor 15:22-28). And if sinless, there would be no need for them to repent in order to be saved from sin. While a sense of grief and remorse for past sins may be possible (and even inevitable), a “change of mind” to cease from present sin would not be necessary. And if this is indeed the case, then it would certainly explain why Scripture can teach very clearly the ultimate reconciliation of all people to God without also having to affirm post-mortem repentance and faith.
I think the idea of faith ultimately becoming unnecessary as a condition for salvation may be supported by Paul’s words in 1 Timothy 4:10. There, the apostle declares, “To this end we toil and strive, because we have our hope set on the living God, who is the Savior of all people, especially of those who believe.” Now, one might want to be the savior of another person, but unless this desire is certain to be realized in the actual salvation of the person one wants to save, one cannot properly be called their “savior” without emptying language of all meaning and sense. God is the Savior of no more than he saves or will save. And since Paul is careful to single out believers as a subcategory of the “all people” of whom God is the Savior, then the only other category of people is, of course, “unbelievers.” Thus, Paul seems to be saying that God is the Savior of believers as well as unbelievers.
Before expanding on this point, it’s necessary to first understand how God can be called the Savior “especially” of those who believe. To do this we need only look to a similar statement made by Paul to the Galatians: “Therefore, as we have opportunity, let us do good to all, especially to those who are of the household of faith” (Gal 6:10; cf. Titus 1:10; Philemon 16). Now, is Paul saying that we are to “do good” to those who are of “the household of faith” at the exclusion of all others? Or, is Paul saying we are to do good to all people, but that those who are of “the household of faith” should be our first priority (since the “household of faith” are with whom we are in community)? Obviously, the latter is the apostle’s intent. Those who are our brothers and sisters in Christ ought to come first, though we should make the best of the opportunities God gives us to help all people who are in need - even those people who dislike or hate us. Similarly, God may be called the Savior “especially of those who believe” since it is believers in the gospel of Christ who have presently been granted the repentance that leads to “a knowledge of the truth” (2 Tim 2:25), and have consequently begun to enjoy the salvation that God appointed Christ to ultimately bestow upon all people. But this salvation that believers presently enjoy by faith does not in any way diminish or subtract from the salvation that all people are certain to receive from God at a future time.
Now, as stated earlier, the assumption inherent in the views of many who are opposed to UR is that, in order for those who die in their sins to be saved after they die, they would have to repent and believe. And since there isn’t any verse or passage that explicitly states that those who die in unbelief will in fact repent and believe after death, it is assumed that those who don’t repent and believe before they die will never be saved (though, it should be pointed out, Scripture never states this). But if God is the Savior of both believers and unbelievers (as seems to be implied in 1 Tim 4:10), then this assumption is shown to be invalid. If everyone must believe in order to be saved by God, then it would not be true that God is “the Savior of all people, especially of believers.” He would be the Savior exclusively of believers. Thus, it would seem from this statement that faith will not be necessary for everyone to be saved by God; it is only necessary now.
I should also add that, at the end of 1 Cor 15, Paul seems to imply that sin (which he identifies as “the sting of death”) will be absent from all who are to be raised immortal by Christ (1 Cor 15:54-57). If this is the case, and if all are to be raised immortal by Christ, then it follows that all are to be raised in a sinless condition. Consequently, repentance and faith would no longer be necessary conditions for salvation, for those resurrected will already have been saved from everything they need to be saved from.
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(I have time–the little kiddos are watching a movie with dad, and the bigs are off at a slumber party!