HELP! Am I missing something, or what?

I've been pondering this for weeks, and I feel like I must be missing something blindingly obvious - and fear looking stupid.

But.

This business about public spending being used to stimulate the economy. Somehow it makes no sense to me. Seems to me it's a closed system - the money to perform that public spending comes from taxes and borrowing, so surely it can't create growth?

If anything, it makes things worse, because a lot of that spending will be on Gordon's HMG AmEx.

Enlighten me, someone?