Earlier quoted context omitted.
Some people actually get paid by the federal government. When these people don't get paid, they are much less likely to spend money, hurting non-government businesses. And the parts of the government that are shutting down also won't be consuming from private business either, again hurting business and the economy.
Your making the broken window fallacy: http://en.wikipedia.org/wiki/Parable_of_the_broken_window If we didn't have these unwanted government services (or wanted services provided very poorly or at excessive cost), then the taxpayers would spent their money on something else -- something that is wanted -- and it would generate just as many jobs or economic activity in some other way.
Besides, which services do you believe are "unwanted?" I agree there are many unnecessary "paper pushers" and managers, but the shutdown affects entire departments. One can't simply stop paying the redundant middle managers, and continue paying prison guards and air traffic controllers.