My guess is when Larry Summers met Sen. Elizabeth Warren, he finally realized that he would not convince her for his candidacy. She is the 'bell weather' senator for Left on Financial Matters. White House thought Summers qualified and potentially very useful to President Obama in circumstances like when GOP is controlling both houses of Congress and forcing to adopt economically detrimental policies. In such scenarios Summers would not be easy to stream roll or intimidate and Summers led Fed would work as the 'backstop' for all the sabotaging Republicans would do to American Economy. But once Summers realized that he does not have necessary critical support among Democratic Senators; he did the right thing by withdrawing nomination. Just after Syria Congressional Authorization brawl, one more fight with Congress would not have helped President Obama any further.
Already there are doubts about how Democrats are not 'united behind Obama'. What all this means is despite the talk of 2016 is far away in future, American Politics is slowly re-grouping / re-aligning for the post-Obama Period. And the safest bet for politicians in that situation is to become 'populist'; Dems rushing to drop any Centrist politics and going to the safe bet of Left politics while Tea Party going full tilt on Conservative side. If indeed, talk of 'increasing inequality' catches the fire (having seen the peak of pro-rich agenda in Romney-Ryan ticket of 2012); Dems may be simply going to older agenda. Votes for New York Mayor candidate Bill de Blasio indeed show that - the hard Left turn to earlier policies.
The danger in all this is further polarization, assuming there is still room to go extremes without breaking this union! One just has to look at how Colorado successfully recalled gun control advocating state legislatures. All this means, Blues will go more popular on Left side and Reds will go more popular on Right side. No more 'tough votes' of any sort in Congress.
I do not think President Obama has any choice here. He has to bow to the wishes of his assertive Left Base. Else nothing, nothing at all will be achieved in remaining years of this Presidency; the Presidency which is looking lot weaker in the very first year of the second term. You cannot swim against the public pressure, if you intend to preserve some political capital to be used at right time (like say attacking Iran without Congressional approval if in the end there is no peaceful solution for Iranian nuke pursuit).
As far as the business of governance goes, President Obama should simply accept Janet Yellen as the Fed chief. That should make the base happy and no surprises to Market. Sure it has the feel of picking up 'second best choice'; but when you do not have marbles, you accept the reality as is. The only other choice worth risking would be ex-Israeli chief banker Stanley Fischer; Ben Bernanke's teacher who has sterling reputation in central banking circles.