First - Krugman is wrong to say that sub-national cross-sectional studies are good for estimating multipliers. I've explained this several times before in critiques of papers producing multipliers that I "like" and "don't like". There are a couple major reasons why this sort of estimation strategy is a bad one:
(1.) Demand spillover means that any impact on demand in one unit is going to raise demand in other units. It's not just interstate commerce either, particularly since Krugman is looking at county-level data here. Once you get to that level, labor markets matter a lot too. My wife and I live in Arlington County, Virginia, but we both work in Washington D.C..
(2.) One of the most important impacts of fiscal stimulus is what it does in the loanable funds market. This market is national (international, actually), so it's going to be a wash in county-level comparisons. Remember - when you're comparing changes at the level of a geographic sub-unit, you are estimating effects off of the variation between those sub-units. The interest rate may vary between those sub-units, but not as a result of anything going on with fiscal policy.
Scott Sumner doesn't lay out this case against Krugman exactly - he just throws around "fallacy of composition" and "correlation is not causation" - but even in his criticism of Krugman I think he goes too far. The paper which Krugman cites that produces the 1.5 multiplier he's interested in actually is a fairly appropriate use of geographic sub-units in my opinion. The question that Nakamura and Steinsson ask is "what is the impact of fiscal policy for geographic sub-units within a monetary union" (presumably with Europe in mind). If that's what you're interested in, then county-level comparisons are a great idea because you want to difference out the impact of monetary policy and the impact of fiscal policy on the loanable funds market. The only criticism I can think of is that they use military procurement - which is a federal expenditure - so they can't capture the impact on the public finances of geographical sub-units (which may be relevant). Aside from that, this is a very appropriate use of county-level comparisons. That does not mean that Krugman is right to praise the method in general. It's certainly no good for measuring the effects of ARRA - as some have tried to do.
I also think Sumner is way too strong in criticizing the Sufi and Mian study that Krugman introduces in the first place, which isn't even meant to estimate multipliers. Sumner argues that if tight money caused the problem in the first place, housing sector indebtedness is a spurious cause. That's a little much. Look, there's disagreement over whether tight money is the primary cause of financial troubles, or whether financial troubles caused the tight money. This county-level analysis by Sufi and Mian can't answer that chicken-and-egg question. But it can verify the importance of balance sheets as one link in the chain, so I think Sumner needs to back down on this one. Unless Krugman claims "tight money is definitely not the problem here", he doesn't seem to have said anything out of line with respect to the Sufi and Mian study. Krugman is quite sympathetic to the idea that tight money causes recessions, I think.
What readers need to be careful of, though, is assuming that geographical sub-unit analysis is a panacea for multiplier estimation - it's not.