Robert Barro, Harvard professor, former Rochester professor, and strong candidate for a future Nobel Prize in Economics, has one of the best explanations of the concept of the multiplier effect in his WSJ article today.
Team Obama is doing their math with a multiplier of 1.5. That suggests that government spending will add one-and-a-half times its own value to GDP, without displacing any private production. Barro's own estimates show that wartime spending has a multiplier of 0.8, and peacetime multipliers have not been significantly different than zero. That is, in peacetime, government stimulus spending is completely offset by lowered private production. Society gets zero net benefit, and government debt rises.
If this is hard to understand, read Barro's article, which explains the concepts at greater length and with more fluency.