I guess it could've been phrased better as it costing the government $600 to give the contractor $20 for a hammer. I'm under the impression that there is a cost to running the government, itself, and that it can be terribly inefficient in how much it costs it to spend money to buy things. I don't know how bad it is, and I doubt it really costs $600 for a hammer, but I don't think that all of the "spending" (or costs) of the government contributes to private income.
Well, as NoNukes points out, it has to go somewhere. In the end,
people get the money, it doesn't get thrown into some big pit.
If the government was not only wasteful, but also venal and corrupt, and the other $580 in your hypothetical example went on whores, drugs, and gambling, it would still be the case that every dollar would end up in someone's pocket.
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