Economic Stimulus Package

I just don't see the advantages of the proposed economic stimulus package set for this summer. The typical taxpayer will receive a check for $800, at the expense of the US government. Won't the net effect here be zero? Most people will probably go out and spend it, help small businesses, and boost the economy, but the government will be out $145 billion. Personally, I'm planning to put this money in the bank. I know it's not the intent of the package for people to save the money, we're supposed to go out and buy a new TV or something. But it's only 800 bucks, it's not like I can go out and buy a new truck with it. What am I missing? Offset recession by increasing the national debt? Does it work that way? Obviously, more study on my part will be needed.