One more point that's worth making about all of this: discussing fiscal stimulus is not the same as arguing whether FDR prolonged the Great Depression, or shortened it--a very complicated discussion I'm not prepared to have right now. When you ask whether fiscal stimulus shortened the Great Depression, you should be simply asking
1) Was there a fiscal stimulus
2) Did it shorten the Great Depression?
The tenative consensus answer is that the stimulus was small compared to, say, 10 years later, and that other factors probably contributed more than the fiscal stimulus.
But "other factors" were some things that FDR did. His bank holiday may not have been the best way to handle the crisis, but it handled the crisis, and ended the disastrous second banking panic. The FDIC, FSLIC, and so forth were created on his watch. Conservatives often write these bits out of the New Deal in order to argue that FDR's other actions prolonged the Great Depression, but these, too, were part of the New Deal. I'd say NIRA indisputably prolonged it, FDIC et. al. certainly shortened it significantly, some of the stuff he did was foolish but not really relevant (gold purchases, I'm looking at you!) and other things, like fiscal stimulus, are hard to measure. On net did the New Deal prolong the Great Depression? I view the banking reforms as dispositive, and NIRA didn't last that long, so on balance I'd say no, but that's a long and complicated dispute.
To be fair, liberals also conflate all the things that FDR did with "massive government spending programs", and it's equally wrong. It is not arguable, in my mind, that FDR's biggest contribution to fixing the mess was fixing the banks, not building dams. But the national narrative puts the FDIC somewhere down there with paying writers for taking oral histories of sharecroppers, and elevates the massive public works projects to center stage.
It's also important to point out--which I've done, like, eighty times--that this is not an argument over works projects. It's a technical question: how much does fiscal stimulus do to counteract a really nasty depression? This matters in part because we're not going to build the Hoover Dam again, and we don't need to--we have social insurance to deal with unemployment in a way that we didn't then, and so we don't need to create make work in order to keep people from starving.