Speaking in the broadest sense, when an economy goes into a recession there are really two major tools that the government has to try to break out of the cycle and encourage economic growth (much of this has to do with the work of Keynes; especially his later work rather than his earlier, simpler models). The first is to cut taxes and the second is to increase spending. The goal of tax cuts is to increase consumer purchasing power and to create greater incentives for employment. The goal of the second is to increase demand as the government buys goods and services, which in turn then drives up employment and increases economic output. The U.S. government has employed these means at different times in our economic policy history, certainly most notably at the end of the Great Depression but also several times since.
The current stimulus package is (again, at least on the broad level) a combination of these two means. It does include both tax incentives and government spending policies. That said, there are a number of reasons why this package will likely cause more harm than good. The first goes back to U.S. economic policy history. One of the necessary conditions on this kind of government intervention in a market economy is that it must be a short-term intervention to break the recession and then government spending will be cut (with or without tax increases). The obvious reason for this is that decreased revenue coupled with increased spending is going to lead to increased borrowing. Normally this is not a problem for the United States as there is no shortage of lenders who love the security of loans to the U.S. Government. The problem is that the government begins to eat up capital that needs to be available to businesses. This has a long-term effect of reducing innovation and slowing economic growth. The fact is that historically many times that the government has intervened in the U.S. the increased spending has not been cut after the economic crisis has ended. This has led to the government, a relatively inefficient economic agent, dominating an ever increasing portion of the market. The consequence is that future interventions become less and less effective and so must be more drastic in scope to accomplish anything. President Obama's stimulus package is equal to the combined cost of the New Deal, the Korean War, and the Marshall Plan after adjusting for inflation. Think for a second about how much money that is and how much borrowing it requires!
Another more recent problem that has come to light is that government spending is actually relatively harmful to economic growth. President Obama's advisors seem to assume that a one unit increase in government spending will actually lead to a more than one unit increase in total economic output (see the Barro article below on this). Several statements have been made about how this package is a kickstart that will encourage consumers to spend more in addition to the government spending increasing. There is simply no empirical evidence for this. Instead a careful examination of the data suggests that times of increased government spending actually causes the economy to contract, again because the government is a relatively inefficient economic agent. So we will not see a one-to-one (or greater) increase in economic growth from spending in this stimulus package we will like see an increase that is much lower or even zero. The long term effects will actually be economic contraction.
Fortunately you don't have to take my word for it on this. Here are a number of links that are quite informative:
"What GOP Leaders deem wasteful in Senate stimulus bill" (CNN)
"Macroeconomic Effects of Senate Stimulus Legislation" (Congressional Budget Office - please note that these estimates are made available to all of your Senators and Congressmen regardless of party affiliation)
"Government Spending Is No Free Lunch" by Robert Barro in the Wall Street Journal (Dr. Barro is a tenured professor of economics at Harvard University specializing in macro and Keynesian economics)
"An Interview with Robert Barro" (The Atlantic) - Here's a great quote on the stimulus package:
This is probably the worst bill that has been put forward since the 1930s. I don't know what to say. I mean it's wasting a tremendous amount of money. It has some simplistic theory that I don't think will work, so I don't think the expenditure stuff is going to have the intended effect. I don't think it will expand the economy. And the tax cutting isn't really geared toward incentives. It's not really geared to lowering tax rates; it's more along the lines of throwing money at people. On both sides I think it's garbage.
So what should we do instead? First I'll point you to an economic answer. This is a suggestion put forward by Dr. Greg Mankiw, also a professor of economics at Harvard. I think that this is a much more economically reasonable proposal that actually has some regard for empirical evidence as opposed to wishful thinking.
Second, I want to point you to a theological response. This article by Carl Truman, professor of church history and historical theology at Westminster Theological Seminary, was written in response to the bank bail out bill (note that this was under the Bush administration so I'm not just picking on either political party, both are at fault). Trueman reminds us of several things when it comes to economic depressions and financial failures. First, all of this is a result of human sin. No matter what economic policies we pursue they are simply the best option given a sinful world. Second, our economic markets reflect human fallenness. The pornography and abortion industries demonstrate again the sinful desires of a sinful humanity. I highly recommend reading this essay though it is a bit dated with what Trueman was focused on.