"For every $1 the government doesn't spend, economic activity shrinks by as much as $2."
from Insights on Stimulus, Thanks to the Mafia
This insight comes from an Italian study showing that when they freeze spending for government project in areas where Mafia corruption was found, the reduction in government spending leads to an even larger decrease in economic activity in the region than the amount of the initial cut. Not only do private sources not step in to make up for whatever the government doesn't spend, but without the government project there is even less private spending than there would be otherwise.
There are, of course, limits to how much the ratios seen in that study will match the ratios one would see elsewhere, such as in the U.K. austerity programs or the massive budget cuts that the GOP is attempting to foist upon the American people. However, the general mechanism will apply. When you're looking at useful infrastructure improvements [roads, rail, bridges, etc.] and/or programs upon which businesses rely for stability -- such as having their healthy, able-to-work labor supply not bogged down with personally looking after their grandparents -- [Social Security, Medicare, etc.], these things will generally hurt economic activity if government significantly cuts spending.