As I've argued before, if the Obama administration was motivated by gender considerations alone, they should have chosen Esther George of the Kansas City Fed; as this article notes, she's an inflation hawk and critical of the zero-interest-rate policy. But her beliefs don't fit in with the Keynesian orthodoxy that grips the ruling caste - those of the "things are bad now but they could have been much worse if we hadn't dug a bigger hole." And besides, why should gender considerations factor into who runs the printing press?
Instead of a new direction and a Volcker-like leader, we're going to get more of the same, much much more. A new Fed chair who believes that the Fed should tinker with the money supply as a means to a whole slew of policy objectives, including growth, employment, inflation, hell probably even the exchange rate (this must be what's meant by the fungibility of money - if you print more of it, it can take care of everything!!). Central bank independence, as I've argued elsewhere, really doesn't matter if the policies are going to be horrific no matter who carries them out (man or woman, Republican or Democrat). And that's what we're looking at right now - a Central Bank that's actually taking its "independence" to agitate for even worse policies.
To paraphrase Ben Franklin, those who sacrifice price stability for higher employment get neither.