Many Keynesians assume that monetary stimulus is ineffective during a liquidity trap. Krugman definitely does not believe that, indeed he specifically argues that only conventional monetary policy tools are ineffective in a liquidity trap. He acknowledges that unconventional tools (such as an inflation target) might be highly effective, but also that they might be politically unacceptable.
As I read Krugman, his attitude seems to be something like the following (which is my interpretation, not his words):
"Ah, what a pity it is that these conservative central banks aren't willing to commit to a modest amount of inflation. That would be the easiest way to boost AD, and the least costly. But as they aren't willing to adopt effective policies, we can assume that monetary policy is ineffective. Now let's move right along and look at fiscal policy."
