But shouldn't the resulting dead weight loss offset any growth in GDP due to larger government expenditures?
When the government spends money (even money it doesn't have) it does grow the economy. Things are still being bought and sold. Money is still exchanging hands.
The problem of the government spending money is that it is often done for political reasons instead of economic reasons. This causes resources to be allocated inefficiently. Is this the dead weight you speak of?
When (rational) private entities spend money it is done for economic reasons. This causes resources to be allocated most efficiently.
The more efficiently resources are allocated translates to a better overall standard of living. Incidentally, this is why outsourcing isn't the bogeyman so many think, it is merely allocating resources more efficiently. You may have to get a different/less paying job but everything will be far cheaper. Your salary/cost of living ratio will ultimately be less.