...while the zero bound does not bind, the Fed might nonetheless be reluctant to engage in the appropriate amount of monetary expansion, and that a fiscal boost is therefore required. A potential response to this is that if the Fed has chosen the unemployment rate with which it is satisfied, it will simply offset any fiscal measures to push unemployment below that level.
Plausibly, the Fed may believe that inflation caused by fiscal stimulus, and not offset by higher interest rates, will not damage its credibility in the way that large-scale QE might.
In fact, I believe this describes exactly the Fed's current attitude. Even if it's not Bernanke's personal opinion, we can infer a "collective attitude" from the joint behaviour of the Fed governors. In which case, fiscal stimulus is probably justified.