John Cochrane makes a good argument against Larry Summers that I've made here before that you simply can't use cross-state studies to talk about a national stimulus package. You could - perhaps - use those studies to provide some insights into national stimulus in some Eurozone country. But even there you have to be careful about what you're looking at exactly.
My concern with Cochrane's discussion is that it conveniently only goes through the things that would bias these estimates upward (thus producing overstimates of the multiplier). There are other reasons to think the estimates could be biased downward, producing underestimates of the multiplier. Cochrane should be up front that both are in play. But the point remains that cross-state studies are going to give you pretty crumby estimates and you can never be quite sure what to make of them.
Mark Thoma, though, also pushes back on Cochranes citation of crowding out and highlights none other than John Taylor pointing out that there's no reason to believe stimulus spending will completely crowd out private investment (it would kind of defeat the point if it did!).