As a follow up to the prior post, I will say that I think one of the things that does make people so emotional about discussing stimulus is that probably 95% of us learned in high school a narrative that most economists seem to agree is incorrect. Challenging that narrative feels like an act of gross conservative revisionism to those who already found it ideologically congenial.
But as I say, among economists it's not heretical to say that it was more likely monetary expansion and the regeneration of the credit system that created whatever real recovery we saw (Christina Romer's summary is here). It is true that the return to growth in 1933 tracks the election of FDR, and the contraction tracks the decision to balance the budget. The problem is, they also track events in the banking system: in 1933, mostly undisputed good things like the certification of the banks, and the creation of the FDIC happened, and in 1937, the Federal Reserve raised reserve requirements, which of course meant a sizeable contraction in credit.
One thing to remember is that the fiscal stimulus of the 1930s just wasn't that big. At its peak, the budget deficits of the thirties were less than what we ran under Reagan--less than 6%, compared to wartime deficits that ran between 20-30%. You need unrealistically high multipliers to credit FDR with turning things around all by himself, especially since the approach to full employment occurred at relatively low levels of spending; the fastest growth pre-World War II was in 1941, when deficits were far below their 1934 level.
Of course, many people believe that it is spending, rather than deficits, that are stimulative, but they are confusing an argument between forms of stimulus--spending vs. tax cuts--with a debate over the stimulus itself. If you take money out of the system in taxes, and spend it, you've created barely any stimulus at all, because more than 90% of that money would have been spent by private parties. (At our current savings rates, close to 100%). It's borrowing the money and spending it that creates the stimulative effects.
Another thing to remember is that either theory is heavily tainted by post hoc ergo propter hoc analysis. Financial crises do get better, eventually, whether in tight-fisted Argentina, or bridge-to-nowhere building Japan. Whatever you happen to be doing at the time will thus look as if it is decisive. Or as an economist recently pointed out, if you look at any moderately large component of economic activity--Wal-Mart's sales, say--and study it in relation to economic growth as a whole, they will tend to move in the same direction most of the time. This does not mean that Wal-Mart makes the economy grow, or that we could make it grow faster by building more Wal-Marts. Controlling for this is statistically tricky.
This is not to say that there aren't many economists who think that stimulus could have worked--they generally argue that the problem was that it wasn't big enough. But most agree that it didn't work. The works projects may have palliated unemployment, but they didn't make the economy healthy again all by themselves.
My understanding is that historians have a rather different take on things, but in a dispute about the economy, I tend to side with the economists over the historians, for the same reason that I think physicists know more about the laws of physics than the best historian of science. But of course, the historian's version of the Great Depression is more widely taught than the economist version, which is why it feels like I'm saying something radical and heretical when I suggest that the New Deal didn't work in quite the simple "spending in, growth out" way that most people believe. But I'm not really saying anything much different from Paul Krugman, though I'm much more cautious about the marvelous benefits of World War II spending than he is.