Will the fiscal stimulus work -- will the increase in government spending cause GDP to increase and unemployment to decrease?
One of the key issues is what economists call "crowding out". I hate to give just a simple explanation of it, because as you will see, economists have been attacking one another over simplistic (and some not too simplistic) explanations. But anyway, crowding out refers to the possibility that an increase in government spending will cause spending by other agents (especially businesses) to spend less. If that were to occur, then there might be no overall increase in aggregate demand, and no stimulus.
See here for a piece by John Cochrane at Chicago titled "Fiscal Stimulus, Fiscal Inflation, or Fiscal Fallacies?" Gene Fama gives his own thoughts in a new blog feature on the DFA website. See here and here for some rather testy responses by DeLong and Krugman.
It is enlightening to read the comments on either the DeLong or Krugman sites to get a sense for who is reading those blogs.
At any rate, when I was in graduate school at UCLA in the early 80s, crowding out was a huge question. You can address it pretty well by the old IS/LM model. I am not a macroeconomist, but my casual observation from the later 80s and 90s is that the crowding out argument did pretty well, and the standard Keynesian "government spending will increase GDP" result was relegated to the "tired models" shelf, to be brought down in honor only in extreme times. Well, it certainly has come back with a vengeance.
With governments worldwide heading to the capital markets in a real big way, I don't see how we won't get some crowding out. Yes, there is another equilibrium with higher world income and higher consumption, government spending, and higher private investment too -- that is the rosy view with little crowding out and big multiplier. There is a less rosy view, with just slightly higher world income, much higher government spending, and less consumption and investment.