The progressive pack wants to hold him accountable for not "doing more" to fight unemployment (here's David Leonhardt for example).
But, can Chairman Ben do more?
Well in one sense, yes, he could always announce another policy initiative. QE III anyone?
But the important question is can the Fed do anything right now to reduce unemployment faster?
I don't think so.
All the policies Leonhardt mentions require the Fed to make a credible current commitment to an unusual set of future actions (set interest rates at near zero for several more years, create higher than "normal" future inflation).
In other words, for these types of polices to work, the Fed has to change expectations about future Fed behavior.
People, there is a huge literature exactly about the fact that the Fed cannot credibly commit to some future optimal policy (the so called "time-inconsistency" literature).
Fed promises to do strange things in the future simply are not believable and are thus extremely unlikely to produce the desired private sector reaction.
To my knowledge, none of the proposals being floated for the Fed to do more avoids this basic issue, and thus, I do not believe the Fed can do anything at this point to make unemployment fall appreciably faster.