I’m not sure if James Hamilton would call himself a “Keynesian,” but this is exactly what sensible Keynesians should say:

I emphasize that I am decidedly not suggesting
that either fiscal or monetary policy stimulus are capable of solving
all of our problems. Real debt imbalances, both domestic and
international, frictions in moving resources out of housing and autos
and into other sectors, and the profound problems with our financial
system all place important physical constraints on what any stimulus
package, monetary or fiscal, is capable of achieving. Once we get to 3%
inflation, that to me will be a clear indication that we’ve
accomplished all we can with tools to stimulate aggregate demand.

Alas, I predict that when we hit 3% inflation, Keynesians in power will not proclaim, “We’ve done what we can do.  The rest is up to the market.”  I’m not sure whether sensible Keynesians don’t get power, or whether power leads sensible Keynesians to hold their tongues or lose their heads.  All I know is what happens – the underlying model remains a mystery. 🙂