I think that with the current system as it is, we’re stuck with two major parties and as entrenched as the Republicans and Democrats are, it’s unlikely that either will get replaced by another.
I don’t think a one-party system will ever happen, or at least if it does, only briefly, because eventually someone will get nominated by that party that enough people disapprove of that, rather than just supporting the candidate they like most, they’ll find someone they can all sort of agree with, you get a few of those people aligned, and a party starts to form.
I think it’s possible that if enough people get upset with the Republicans, they could end up splintering into different parties, they’d slowly have start to grow and generalize from their stances in order to get more votes and win elections, and we’d end up back in two parties, except perhaps with some of the stances adjusted. For instance, if say the Libertarian party became the kernel that the new party formed around, we might see some of those ideas stay in place, but I imagine with a large constituency of the former religious right wing out there, some party is going to have to court them, which means alienating some others. So it’s possible you could see then end up with that new Libertarian party and them taking on some conservative views, sort of like a partial reboot to the Republicans of the 80s, or maybe latching into the Democrats and then some of the socially liberal minded jumping ship and we get a divide more along views of how much government should do. It’s impossible to say how it might ultimately shake out. But, ultimately, I think any of those are low possibilities.
Of the options given, I think the Democrats fracturing is more likely. As it is now, there’s some fairly conservative Democrats, particularly from Southern areas, and some very liberal ones, so I think we’d more likely see more of a regional divide as the former Republicans have to find a new home and get involved in their local politics.
Really, though, I just don’t see the Republicans going anywhere. Even with the recent criss being overwhelmingly blamed on Republicans, there’s still a large group of people who just plain see the Democrats as every bit as evil as some of those addressed by the OP see the Republicans, and they’ll stick with it since there’s still no viable third party and joining the Dems would be straight up wrong to them. So they’d likely become a marginalize party for a cycle or two, rebrand, and come back. We’ve seen this a couple times in recent history, with the Contract with America in 1994 and the Tea Party in 2010. Particularly if the Republicans do poorly in 2014, we could see them abandon the current course and come back with something new in 2016.