I'd agree with you in theory, it's pretty standard demand management, that the public sector picks up the slack when private sector demand is low.
the problem with a lot of governments, including the US, appears to be the other half of the equation, which is that when the private sector is doing well, the public sector should contract, in order to mitigate the effects of inflation.
What seemed to me to have happened in the last decade is that government costs expanded in the "good times" causing a deficit, and meaning that when the bad times came with the financial crash it's a lot more difficult for them to expand spending.
The other problem (although it doesn't apply as much to the US as other countries) is sovereign debt risk. Countries like the republic of Ireland absolutely have to cut expenditure as otherwise the bond markets see them as a real default risk and hike up the cost of their borrowing, so they have no real choice but to decrease government spending.