We've talked about several of these on here before, but Dylan Matthews reviews nine stimulus studies - six of which say it had a positive effect, one which says it had a modest effect, and two that said it didn't work.
I've got a few broad thoughts on these. I don't like inter-state studies. I doubt we can really say anything about any one recession, unfortunately - I think it's better to just look at the impact of fiscal policy in a recession in general. Papers that don't deal with endogeneity aren't really worth your time. Papers that do deal with endogeneity often have trouble focusing on impacts during recessions. And it's been six or seven years so I have to take another time series class before I express an opinion on VAR studies.