Your telling me all those billions of untaxed dollars wouldn't do any good if not directed by politicians? No, I really don't believe money magically gains a stimulative effect just because it flows through D.C. that it could never have otherwise.
The stimulative effect of money comes from it flowing, not from it merely sitting somewhere. While far from the only tool to accomplish the task, and not always the best tool for doing so, government taxation and spending is one means by which the total flow of money in the economy is increased.