Why have a fiscal stimulus at all? Why not let the Federal Reserve conduct monetary policy? Gary Becker wondered how we all became Keynesians, relying on fiscal policy instead of monetary policy. Brad Delong's answer is that the Federal Reserve has already used up all its tools, and is now close to powerless. It can't push interest rates lower, and it has already dramatically expanded its regulatory powers. It has, at most, slowed the rate at which we slide into recession, rather than reversing it.
This only partially answers Gary Becker's question, I think. That is, it makes sense to resort to fiscal policy if fiscal policy works. Why do we all think it will work?
Fiscal policy could work if government spending employs resources that would otherwise be idle. A multiplier effect could cause wisely-spent government funds to have a large impact, restoring potential GDP, shortening the recession. It is worth pointing out where these unemployed resources are: finance and construction (those are the biggest and most attention-grabbing areas, anyway--we're certainly shedding jobs in automobiles and other manufacturing, too).
A critic (like Kevin Murphy) of a spending stimulus package would therefore suggest that the proposed areas to be stimulated are not the proper areas. That is, building and repairing roads and bridges will not employ out-of-work financiers (although it might employ out-of-work homebuilders). They will not put down their briefcases and pick up shovels. Arnold Kling would, I think, argue that the finance industry got too big, anyway, and that even a stimulus package that targeted finance workers would be a bad idea. We want that industry to shrink, shifting jobs elsewhere. That may not happen in the short run, stimulus or not. We might just have to wait for that adjustment to take place.
A related critique is that much of the proposed spending is either pork or irrelevant to fiscal stimulus. For example, expansion of environmental spending is probably going to transfer jobs from one area to another, rather than employ previously unemployed resources. James Hamilton says that he takes the large lobbying effort by special interest trying to get pieces of the stimulus package to be evidence that it is less about stimulus and more about rent-seeking. I think there needs to be more discussion of these Public Choice issues in this debate than there has been.
A critic might also point out that the multiplier concept is a bit fuzzy. The multiplier is surely not constant, or we could just spend our way to prosperity and forget about economic growth. But if the multiplier declines as spending grows, then how fast does it decline? If it declines quickly, then the stimulus effect will be small. On the other hand, if the multiplier declines slowly, a stimulus package could have a large effect.
Any borrowing to pay for stimulus will have to be paid back at some point, which will require taxes, which have deadweight losses (that is, they discourage production and consumption of the goods that are taxed). This is a general argument against taxes, and therefore against government spending. It might be worth it to suffer eventual deadweight losses if the short-run stimulus effect is large.
Speaking of borrowing, there is also the Ricardian Equivalence problem. If people know that big government borrowing means big future taxes, then they will reduce their expenditures even more now, in order to save money to pay for those future taxes. This will at least partially counteract the stimulus package. It seems to be the case that the tax cuts given last year had little effect, as they were mostly saved (perhaps for the reason explained above), resulting in little stimulus effect. Nonetheless some still argue that tax cuts would have a larger stimulus effect than spending cuts.
Then there is the problem of crowding out. Increased government borrowing may increase interest rates, which causes a decrease in private investment. A business owner might have been considering building a new factory, but increased government borrowing might have increased the demand for loanable funds (or, in Mankiw's preferred form, decreased the supply of loanable funds) , which drives up interest rates, making the business owner less willing to take out that loan to build that new factory. Interest rates are so low right now, though, that I have a hard time believing that a modest increase in interest rates would affect investment.
It is probably the case that, if we waited long enough--perhaps a year or two--the economy would self-correct. It is worth pointing out that the unemployment rate is not really into frightening territory yet--7.2% is not that bad, by historical standards. On the other hand, it is thought that it will go up, possibly as high as 10%, which is pretty bad. There is also an argument that this measured unemployment rate is too low, and that a more useful unemployment rate (which counts workers who have given up looking for jobs, for example) is closer to 13%. One would need to show that this number has been rising more quickly than the ordinary unemployment rate in order for this to be relevant, I think. I'm not sure if that's the case, and I'm currently too lazy and busy to look it up. Keynes thought that this focus on the long run--the idea that the economy would eventually self-correct--was erroneous, since we live in the present, and that if we could smooth the business cycle, we should do so.
So can we? I don't know. I am skeptical. To sum up, there are two basic kinds of objections: theoretical (even if we implement the best possible stimulus package, it won't do much) and practical (we are not likely to get anything close to the best possible stimulus package). For these reasons I think it might be best to simply avoid repeating the mistakes that caused the Great Depression to be more than just an ordinary recession (and I think we've already accomplished that), and let the macroeconomy do the rest. Still, this is in part a debate about magnitudes of effects. How big is the multiplier, and how fast does it decline? How much do people anticipate future taxes when they see current government borrowing? Will government spending target unemployed resources, or will rent seeking cause it to simply shift already-emplyed resources around? How fast will the economy correct itself if left alone?
But I am not a macroeconomist, I dislike macroeconomics, and I do not really understand it, so it would probably be better for you go to read Brad Delong or Arnold Kling or Greg Mankiw or Larry Summers or Martin Feldstein anyone else.