Scott Sumner talks about the good old days of President Reagan and Congressional Democrats compromising.
My own comment is:
Old theory that R. President Reagan and Democratic Congress compromised under:
Cut and simplify taxes for growth (R. Reagan) and added revenue in exchange for more government spending (D. Congress). Everybody gets what they want. If the government wasn't divided, the solution would have been different.
Over time, the D's decided that if you keep cutting taxes the government patronage spending gets crowded out by government debt. (Ignore that government revenue still went up in the Reagan years and other tax rate "cutting" administrations.)
Over time, the R's realized that if you keep spending, private investment gets crowded out by government debt and the government gets bigger, supporting the D's patronage supporters. (Ignore that the R's adopted a big spending habit themselves while in control.)
So of course, the D's solution now turns out to be raise taxes and keep spending, while the R's solution turns out to be cut taxes and stop spending. The old tax rates compromise required spending to buy patronage. Now you have some R. idealists in Congress with enough power to block earmarks and other vote buying based on the spending and patronage model.
So what's the new compromise available to R's and D's that preserves any part of what they want? I don't see it. The old model is dead because political reality has changed.
You could suggest that an effective President could still twist arms and work a compromise, but President Obama doesn't talk to D's in Congress, let alone the R's, unless you count press conferences attacking them for voting down his politically-designed proposals almost unanimously.
Ultimately, the solution to the impasse is going to be the election in November. Until then, a divided government will muddle along. Afterwards, I suppose it will be determined by who shows up to vote in November.
I'll add here that I think if Romney wins in November and the R's continue their track to win the Senate and hold the house, the idealistic R's in the house will still have enough leverage to stop any big increases in government spending.