The Council of Economic Advisers argues for a significant role for the Economic Recovery and Re-investment Act of 2009 in their third report on the topic here. Not surprisingly, they argue for a large effect. And economic theory can support this claim: when interest rates hit the zero lower bound, fiscal policy can be extremely effective at increasing output and welfare, as this recent paper by my colleagues shows. But there is a caveat. Once the zero lower bound is not binding, fiscal policy can be quite wasteful. More generally, we need theory that matches the salient features of reality, such as the spending response to tax rebates that I have studied (see these papers).