Even though the stimulus bill of 2009 was sold as a "shovel-ready jobs" bill, a lot (most?) of the money has gone to shore up existing federal agencies and programs or was sent to states to support state budgets. Here's Hazlitt on why using money to retain government employees (whether you think that's a good idea or not) is unlikely to "stimulate" the economy:
The country is not merely as well off without the superfluous officeholders as it would have been had it retained them. It is much better off. For the officeholders must now seek private jobs or set up private business. And the added purchasing power of the taxpayers, as we noted in the case of the soldiers, will encourage this. But the officeholders can take private jobs only by supplying equivalent services to those who provide the jobs—or, rather, to the customers of the employers who provide the jobs. Instead of being parasites, they become productive men and women.