In the future, I think this will be the big research issue concering the stimulus. It almost surely saved public sector jobs. The question is whether there was any trickle-down into the private sector. The authors suggest that there was more negative trickle-down than I would have expected.
If you follow the left-wing economist blogs, you will see that there could not have been any crowding out of the private sector, because interest rates are not high. That is what happens when you think of the economy as a set of equations drawn from textbooks, rather than thinking in terms of patterns of sustainable specialization and trade.