Nate Silver's qualified answer:

[If] Obama can defeat a Generic Republican with an approval rating of X, he can defeat Palin with an approval rating of X-3. Caveats abound, of course -- this conclusion too is based on some fairly limited evidence. But if you told me that Obama's Gallup approval rating was 45 percent on Election Eve 2012 and that his opponent was Sarah Palin, I'd put my money on Obama and feel pretty good about it.

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