Simon Johnson, Jeffrey Miron, Russ Roberts and Mark Thoma answer the question here.
The fiscal stimulus played a decisive role in reducing the depth and pain of the recession and is now helping to get a recovery under way.Miron writes
The Obama administration and many economists believe the fiscal stimulus package caused the positive G.D.P. growth, but this conclusion is not warranted.Roberts writes
The good news is that third quarter G.D.P. is up. But has government spending (or the tax cuts in the stimulus package) caused the growth or would it have occurred anyway?Thoma explains
It’s hard to say, but there are logical reasons to be skeptical of the impact of the stimulus.
Increased consumer spending accounted for 2.4 percent of the 3.5 percent increase in output growth, and much of the increase in consumption was driven by the “cash for clunkers” and other government stimulus programs.John B. Taylor's answer to the question is here. His title? "National Accounts Show Stimulus Did Not Fuel GDP Growth".