You have the basic identity that (S-I) + (T-G) = (X-M). That is, private net saving plus government saving equals net exports. If net exports stay about the same, then when private net saving goes up, government net saving goes down. The sentence quoted above created a picture in my mind of this happening. I presume that it is a highly abbreviated, and perhaps slightly mis-spoken, way of telling the Keynesian story in which an excess of desired saving over desired investment leads to a drop in income. In the original Keynesian story, the intention to save more does not necessarily result in an increase in actual saving relative to actual investment.
I think that Keynesians need to unpack this story quite a bit more, because it is the heart of their view of the recession. What I believe they want to say is that the process of de-leveraging is highly contractionary. However, there is a lot of institutional and behavioral detail to be filled in, and there are a lot of interesting questions to answer. For example, policy makers acted as if de-leveraging in particular industries, notably banking (also automobiles?), would be particularly troublesome. Is that indeed a factor?
None of this is meant as a fundamental criticism of Krugman's main theme or of the Keynesian outlook. That I have made elsewhere. Here, I am suggesting that within the Keynesian paradigm, the connection between de-leveraging and macroeconomic activity is going to be one of the main items on the research agenda. For now, Krugman writes,
a large number of economists ready and willing to go for good first approximations - quick and dirty but intellectually sophisticated approaches that would let them respond to a radically changed economic environment. Good old-fashioned IS-LM fits the bill, and as I see it the economists who did best in this crisis began with IS-LM, then backed it up later with simplified versions of New Keynesian analysis.
What I am saying that the process of re-telling the IS-LM story is not yet complete.
[UPDATE: not exactly related, but Doug Clement of the Minneapolis Fed looks at the growing literature on non-representative-agent models in economics.]