Good points from Mark Thoma, especially this one:
But the clincher is the fear that if they do end up creating inflation, the Fed could lose its independence, particularly if there is little to show for it in terms of stimulating the economy. If they lose their independence, the response to every future recession would be less effective. This makes recessions more costly, and when the higher costs are tallied across all future recessions, the total cost of losing its independence is very high. Thus, this is a major stumbling block.
Which is to say, we have less an economic dilemma at the Fed than a political one.