Let's get right to it. The Fed has no credibility. Not just now, but in the whole course of its history.
At least not if we define central bank credibility the way the economics literature does (Kydland & Prescott, Barro & Gordon), as the ability to overcome the time inconsistency problem.
This is a fundamental problem of central banking: All the Fed can do is maximize its current period utility function. Bernanke saying we will keep rates low till late 2014 is like Lucy telling Charlie Brown to go ahead and kick the football while she holds it steady.
Since nothing makes the Fed actually do in the future what they say they are going to do, no one has any incentive to believe the pronouncements (Charlie Brown if you are out there, pay attention to this post)!
But you say, inflation targeting worked!
People, inflation targeting is so incredibly powerful that it even worked in countries that DID NOT ADOPT AN INFLATION TARGET!
Here's the abstract from a 2007 paper in the Journal of Monetary Economics (Does inflation targeting really make a difference? Evaluating the treatment effect of inflation targeting in seven industrial countries by Shu Lin and Haichun Ye):
We evaluate the treatment effect of inflation targeting in seven industrial countries that adopted this policy in the 1990s. To address the self-selection problem of policy adoption, we make use of a variety of propensity score matching methods recently developed in the treatment effect literature. Our results show that inflation targeting has no significant effects on either inflation or inflation variability in these seven countries. Further evidence from long-term nominal interest rates and income velocity of money also supports the window-dressing view of inflation targeting.
Inflation and its volatility did not fall in the 90s because the adoption of inflation targeting gave central bankers credibility. "Good luck" is a more convincing reason for the outcomes than inflation targeting.
This point cuts both ways. Yes, it implies that the expectational miracle the market monetarists expect to ensue from the Fed unilaterally announcing a target path for NGDP is unlikely. But it also implies that all the Fed talk about "losing hard-won credibility" and "expectations might become un-anchored" is meaningless as well.
There is no anchor.