They have a new NBER working paper on this topic, here is one key part of the abstract:
Fiscal adjustments based upon cuts in spending appear to have been much less costly, in terms of output losses, than those based upon tax increases. The difference between the two types of adjustment is very large. Our results, however, are mute on the question whether the countries we have studied did the right thing implementing fiscal austerity at the time they did, that is 2009-13.
They also consider, and cannot reject, the possibility that the output declines of recent times were due to additional negative variables, such as credit crunches, rather than higher values for the fiscal multiplier.
I predict this paper will be ignored rather than responded to. For a while now it has been the practice to criticize “austerity” rather than to disaggregate the policies, or describe them with greater specificity, even though that is easy to do. And it is incorrect to describe this paper as defending austerity, rather I read it as being anti-tax hike, and suggesting that “austerity” is not a very useful concept.
There is an ungated version of the paper here.