. A CBS News-New York Times poll found that 70 percent of Americans believe Republicans have opposed those policies for political reasons, rather than because GOP lawmakers genuinely believe the policies are bad for the economy.
I wonder how the questions were phrased...

I think that reveals two key things concerning public views of Republicans and politicians in general. Few seriously believe that the Republicans have an ideological conflict with passing big budgets, and some no doubt do have conflicts with passing big budgets. The public is so cynical as to believe this is a purely political move, and it is, to an extent but it's also an affirmation of some Republicans that they don't believe that the budget it the right idea. They are actually sticking to conservative principles in some form or another.

The Republicans can claim a youth vote just as easily as Obama did. The youth aren't going to always going to swing one way, so if the Republicans can sell it right they could take in the youth vote. Besides, Obama is a President, and like all Presidents after two terms we will tire of him. Besides, no one has ever maintained serious control of Congress (filibuster proof Senate and House majority) during a favorable Presidency.
The Republicans need to be able to embrace Schwarzenegger (California) and Crist (Florida), and get their followers to do so. They are fiscally conservative but they're open on social issues, and that's where Republicans need to moderate, move back to close-center at least.