There has been a distinct change in tone from the Obama team today, as they seem to have become suddenly aware that there’s a real risk that the stimulus plan will either fail to pass, or be emasculated to the point that it doesn’t come close to doing the job. Obama himself has warned of catastrophe if we fail to act, and — finally!– denounced the tax-cut philosophy. Meanwhile, Larry Summers has finally made the point I’ve been pushing for a while — that we’re at major risk of falling into a deflationary trap.

I thought it might be useful to present a bit of evidence behind that concern. The figure above plots an estimate of the output gap — the difference between actual and potential GDP, as a percentage of potential — and the change in the inflation rate. Both series are taken from the IMF WEO database, for convenience, and use data from 1980-2007.

It’s not a perfect fit — this is economics, not physics, and anyway stuff besides the output gap bounces inflation around from year to year. But still, there’s a clear correlation, driven largely but not entirely by the deep slump and disinflation of the early 1980s, and an implied slope of about 0.5 — that is, every percentage point by which real GDP fall short of potential tends to reduce the inflation rate by about half a point over the course of the year.

And right now the CBO is saying that in the absence of a policy action the average output gap will average 6.8 percent over the next two years. Do the math: if anything like the historical relationship between output and inflation holds, we’re looking at major deflation.

OK, maybe that relationship won’t hold — getting to actual deflation may take a deeper slump than merely reducing the inflation rate. And maybe a regression driven in part by 80s data isn’t a good guide to current events. But deflation is a huge risk — and getting out of a deflationary trap is very, very hard.

We truly are flirting with disaster.