One theme that has started to appear in various strange corners is that maybe the US should actually split up as it's now two seriously divergent polities with very different ideas about the fundamental principles of politics.
Two points.
First this is not new - there was an actual war in that part of the world that arose from such a division a few years ago. If you think partisan division in the US is unprecedentedly bad you should try looking at newspapers from around 1800 or the later 1820s, the 1850s, 1870s, in fact almost any time in American history. We are misled because the 1941 to roughly 1986 period was an unusual one in which there was way more bipartisanship than normal (you can quantify this).
Secondly, the real problem right now is divisions within states rather than between them. It's the split between small towns and rural areas on one side and large metropolitan areas on the other that we are talking about. There is a simple (but difficult) solution which is to make the 52 largest metropolitan areas become separate states and separate them from the states they are currently in.
That would leave an archipelago of about 40 predominantly blue islands (with, as David Boaz noted all the concert halls, theatres and newspapers) in 50 or so red seas. Both would have enough of the minority to keep them honest. Also, this would still leave the Senate doing its job of tempering popular enthusiasm but not in quite such an egregious way. make for a lot of fun maps as well.