My colleague Jonathan Chait asks the question, would Obama really be more popular if he'd abandoned his domestic agenda? The answer, Jon says, is no. And, as is usually the case, I think Jon is right. The main reason for Obama's unpopularity is the state of the economy. Policy decisions have played a secondary role. Had he walked away from his agenda, he'd be in just as much trouble. (And if he'd never proposed it? He might not be president.)
One point to keep in mind: Insofar as policy decisions really have hurt this administration, I would argue (as have others) that the rescue packages for Wall Street and the auto industry were the biggest liabilities. People got "bailout" fatigue pretty quickly and came to associate the administration with handing money to people and companies that didn't deserve it, which is a sure-fire way to destroy faith in government.
But the alternative universe in which the government doesn't take these steps is, most likely, an alternative universe in which the economy is worse. Maybe a lot worse. It's hard to see how, in that universe, the political situation for Obama and the Democrats is better than it is today.
Update: Nate Silver has a longer, smarter, and more complicated version of this argument.