The Masonists and Cato folks make it sound like it is impossible for the stimulus to be a stimulus. If you take out one gallon of water from a bucket, and pour that water back into the bucket, nothing has changed. If you take a dollar out of the economy and then put it back in, nothing has changed.
It can change the economy though, as Hal Varian points out. In an ideal world, the increased savings would be translated instantaneously into higher private investment (using banks as intermediaries). However, in recessions, and especially the Great Depression, these savings tend to accumulate as cash and not used in any fashion by the economy. This is akin to taking wealth out of an economy. When the government induces people to buy government securities instead of accumulating cash, and using that money to provide public goods, the stimulus can work.
Not that I'm for the stimulus package. I don't think we need it. The Bootleggers and Baptists effect will ensure most of it is a deadweight loss. Besides, printing money is better, and Bernanke knows how to do that. So let him.
Let's be honest about the economics of the stimulus package though. Economic theory does contend that it can have a positive effect, and in recessions, generally will.