One thing that has happened since the civil war is that, at least from where I live, people are much less likely to identify strongly with their state as opposed to the federal government. Don't get me wrong, I really like Texas and I love shoving how awesome it is into other state's faces, but I don't feel a political affiliation with it in the same way I do with the Fed.
Because of that, I'd say it would be extremely unlikely that the US should break up into minor states any time soon. People in America might have their (perhaps overblown) differences, but one thing is certain: virtually all of us like being American. It would take something truly shocking to break that.