First off, here's an excellent interview from a well-respected economist, Thomas E. Woods, that summarizes my response, as a prelude to my answer:
MP3: awr.dissentradio.com/08_12_18_woods.mp3
So, does government spending help the economy? If Bush's last eight years hasn't made it obvious, absolutely not. Keynesian economics are what prolonged the 1929 recession, and made it a depression. All it is, is a redistribution of capital rather than an expansion of it. It's usually redistributed into less productive means, a net loss for our prosperity. Unfortunately, you can't see the destruction that is taking place because of the misallocation of resources, but it's still very much there! Capital (i.e. wealth) can -not- be created by borrowing, taxing or printing money! It can only come from working and saving.
We got out of the Depression -DESPITE- all the government spending and policies Herbert Hoover and FDR enacted, not because of it. Protectionism crippled our exports. Taxes were raised, leaving even less capital for us to fight over. Minimum wages were substantially increased, causing skyrocketing unemployment. Ultimately, World War II had not even solved the issue, as again, government spending can not possibly create jobs. Unemployment went down because 10 million men were drafted. It ultimately ended when all the skilled labor returned from war to work in 1946, yielding an economic boom, as Thomas Woods states.
I'd suggest reading Murray Rothbard's book on the Great Depression to understand why we got into the depression to begin with:
mises.org/rothbard/agd.pdf
Summarizing the book:
mises.org/tradcycl/econdepr.asp
A related article:
mises.org/story/3234
They come from a line of economists over at the Mises Institute that understand full well why we're in this current financial crisis, and the remedies for it. The fascists/statists/socialists that dominate both political parties would have you believe that it's only through their brilliance will we recover from crises, rather than getting back to a solid base of working, saving and self-reliance. Wars, giant infrastructure projects, and government spending are certainly not the way to prosperity-- they're a road to disaster!