Yeah, after 1856, the party system has matured. One thing you could think about are changing coalitions. What if the fiscal conservatives are ignored in the GOP? Well, 30 years from now, you could have a libertarian democratic party and a communalist republican party, rather than a liberal/conservative divide.
I doubt it; the Democrats hold economic progressive/socialist ideas too strongly to possibly become a true 'libertarian' party, at least not in the next century or so. The vast majority of the "liberals" would not consider voting for a communalist party, because of opposition to religious values. Together, they are likely to continue to hold a left-of-center economic viewpoint. They might manage to intimidate true libertarians into voting for them (by comparing themselves to the Republicans), but they'd never be accepted as the 'mainstream'.
However, the Republicans going authoritarian seems quite possible, ditching economic conservativism and taking up 'Godly' values to hold the South and Midwest in line. It isn't the only possible path for them, but it certainly is an option.
The end result, unless a viable libertarian or right-libertarian third party becomes a major force, will be no less than the economic ruin of the nation, as capitalism is continuously blamed for the nation's problems, and the political establishment uses business as a boogeyman to get voters to hand control over for them (even though big business will do just well, thank you. Small business, on the other hand, will be practically dead). I can easily see this resulting in a nearly-collapsed United States falling to either religious fascism or pseudo-communism, perhaps even some truly evil combination of the two.