Back when the stimulus was being considered, there was a lot of talk about what the multiplier of stimulus spending is. Basically, the multiplier is the effect of government spending permutating through the economy: I buy a wrench for my fighter jet from you, you hire workers, they feel richer and start shopping big screen televisions, and so forth . . .
If the multiplier is greater than one, stimulus spending has a big effect; you cause the economy to grow by more than the amount of the government spending. Theoretically, if the multiplier is large enough, and the growth occurs in the right places, you can get enough tax revenue to pay for the stimulus spending. Sadly, empirical estimates are much smaller than the 3x or 4x multiplier you would need for this to be true.
If the multiplier is one, the stimulus basically raises GDP by exactly the amount of government spending.
If the multiplier is less than one, the stimulus raises GDP by less than the amount of government spending. Since you have to pay back the full amount later, and the stimulative effects are only temporary, this is probably not a good deal. Not that this ever stops the government from doing other sorts of spending--F22, I'm looking at you . . .