Bruce Bartlett offers a lengthy history of the 1937 fiscal contraction, and why it wasn't such a good idea. (Short answer: unemployment shot back up and finished the decade in the high double-digits). He worries that Obama may be making the same mistake, withdrawing spending too soon from an economy that is still growing slowly.
I think this is a worry that we should take seriously. But here are some reasons you might not worry so much:
1) 1937 featured a double-whammy of fiscal and monetary contraction. Provided that we stagger the contractionary actions by the Fed and the feds, things shouldn't be quite that bad.
2) We may not need the extensive stimulus that the Great Depression demanded, because we didn't commit the cardinal sin of letting the banking system collapse in on itself. Supporting the banks probably had other costs, but unemployment in the 25% range was not among them.
3) A double dip recession may be inevitable at some point, because we can't continue fiscal and monetary stimulus forever. If 2012 is too soon, that probably means it can't be avoided--in which case it's not obvious that "later" is better than "sooner" to absorb the blow.
Update: Apparently, I heard wrong, and it starts in 2011. That's infinitely more worrying, though caveats one and two still apply.