The Eastern and Western States are different as well. The Mountain and Plains States are different from the Northeast or the West Coast. A country as big as ours is bound to contain very different regional cultures.
Right now, politics are more polarized than they have been at some other periods in our history, but the way that people in different parts of the country live is a lot more uniform than was true in the past. The split is more urban vs. rural than North vs. South, with people in Northern and Southern metropolitan areas living similar lives that are different from rural Americans.
350 million people ruled by 535 that try to shoehorn the entire population into politically correct federally run programs/services/etc is wasteful, ineffective and destructive to life, liberty and the pursuit of happiness.
Breaking up the country isn't likely to retard or reverse current social trends. Cutting Washington out of the picture wouldn't necessarily mean less of a regulatory-welfare state, since people might at first be more comfortable giving power and money to a new government that purports to be closer to their own interests.
What breaking up the country would mean is a loss of American influence in the world and an end to American self-confidence. For better or for worse, whatever successor states arose wouldn't be able to play the role of "World Leader." Sure, there's a burst of exuberance among people who are finally free from the other part of the country, but when they realize how little America and its values will count in the world, or even at home, it will be quite a comedown.
Living in a police state is also quite the comedown.