Does the Fed really have a commitment problem?

This is a followup to my last post:

Here is a more nuanced explanation of Krugman's views on monetary stimulus at the zero lower bound, which I think I had already understood and mostly agree with.  I differ from Krugman (with admittedly little authority) in thinking that it shouldn't be hard for the Fed to make a credible commitment to future easing if they wanted to.  If Bernanke said the word, and explained precisely how he would do it, I believe markets would respond immediately, and the broader economy wouldn't be far behind.  Continued market movements in response to Bernanke's leanings are a hint of that influence.

Yes, it's true, if Bernanke did it Congress would howl in protest and haul him up to Capital Hill and berate him for debasing the currency, etc.  So?  They're doing that anyway. And if Romney wins Bernanke will lose his job and his influence anyway, despite being a Republican.

A long time ago (almost 2 years!) I explained my reasoning about the commitment issue.  I was similarly befuddled by Robert Hall's take on it.  (Also see the update at the bottom of this post.)

The political, intellectual and philosophical obstacles of what Krugman describes as the "first stage" strike me as the greater challenge, which is why I was critical early on about his discussing this less than stimulus. It seemed to me that stimulus of the necessary magnitude was never politically viable, and Krugman had more sway with intellectuals---the FOMC---than with political calculations around stimulus.  And he can use his fabulous writing skill and wide influence to explain the issue to the broader public.  His magazine piece seemed to shift toward this emphasis.  But that was just six months ago.