Paul Krugman believes it is a slam dunk. It's probably a bad idea to argue with a Nobel prize winner, but my understanding was the science was not quite as settled on that point as Prof. Krugman would have us believe. Below the fold I'll cite a few pieces of research on the topic.
First piece - Christina Romer, What Ended the Great Depression, (The Journal of Economic History, 1992). Abstract:
This paper examines the role of aggregate-demand stimulus in ending the Great Depression. Plausible estimates of the effects of fiscal and monetary changes indicate that nearly all the observed recovery of the U.S. economy prior to 1942 was due to monetary expansion. A huge gold inflow in the mid- and late 1930s swelled the money stock and stimulated the economy by lowering real interest rates and encouraging investment spending and purchases of durable goods. That monetary developments were crucial to the recovery implies that self-correction played little role in the growth of real output between 1933 and 1942.
A second piece in the The Journal of Economic History gave a dissenting view - J.R. Vernon, World War II Fiscal Policies and the End of the Great Depression, (The Journal of Economic History, 1994). Abstract:
The United States economy completed its recovery from the Great Depression in 1942, restoring full-employment output in that year after 12 years of below-fullemployment performance. Fiscal policies were not the most important factor in the 1933 through 1940 phase of the recovery, but they became the most important factor after 1940, when the recovery was less than half-complete. World War II fiscal policies were, then, instrumental in the overall restoration of full-employment performance.
Of course, Paul Krugman is aware of this literature. Paul R. Krugman, Kathryn M. Dominquez, Kenneth Rogoff - It's Baaack: Japan's Slump and the Return of the Liquidity Trap (Brookings Papers on Economic Activity, 1998):
It seems to be part of the folk wisdom in macroeconomics that thisis in fact how the Great Depression came to an end: the massive onetime fiscal jolt from the war pushed the economy into a more favorable equilibrium. However, Christina Romer contends that most of the output gap created during 1929-33 had been eliminated before there was any significant fiscal stimulus. She argues that the main explanation of that expansion was a sharp decline in real interest rates, which she attributes to monetary policy (although most of the decline in her estimate of the real interest rate is actually due to changes in the inflation rate rather than the nominal interest rate). Indeed, Romer estimates that for most of the recovery period ex ante real rates were sharply negative, ranging between -5 and - 10 percent.
My point is that the end of the Depression, which is the usual, indeed perhaps the sole, motivating example for the view that a one-time fiscal stimulus can produce sustained recovery, does not actually appear to fit the story line too well. Much, though by no means all, of the recovery from that particular liquidity trap seems to have depended on inflation expectations that made real interest rates substantially negative.
That final piece is 12 years old, so there may be some research since then that has 'sealed the deal' on the theory that World War II fiscal stimulus 'ended the depression'. And of course, there is the point that 'by no means all' of the recovery can be attributed to monetary policy. But I am not aware of any post-1998 studies that have put a great deal of weight on fiscal stimulus as driving the U.S. economy out of the Great Depression. If there are any macroeconomists in the house that have followed that line of study closer than I have, I would love to hear from them!
Edited to Add: I found links online for all 3 of the papers, so I've added those.