I think Matt Yglesias makes a good point here, saying that "the larger issue is that influence in a White House staff job comes from the President deciding he wants to listen to what you have to say" (his emphasis). Fair enough. Larry Summers, former Treasury Secretary, wasn't going to join the administration unless he was going to be a major player, and as Yglesias points out the details of how the National Economic Council chair job worked in the Obama White House were designed with that in mind. So it's fair to say that whoever replaces Summers might be a lot less influential.
However, one can take that line of thinking too far. It's also true that the job actually does have responsibilities; this isn't the Kennedy or FDR White House, in which a bunch of presidential assistants have relatively undefined responsibilities. As I said earlier, the core of the job is to try to keep the dozens of departments and agencies that have responsibility for some piece of economic policy to actually work together successfully, preferably in an attempt to formulate and carry out the president's policies, despite the obstacles of bureaucratic inertia, policy differences, and simple confusion and chaos. In other words, while I think Yglesias is correct that the president will listen to whoever the president wants to listen to (although part of the NEC chair job entails affecting which of the many voices the president hears in the first place), the job of coordinating policy is critical even if the NEC chair acts more as an honest broker and does no policy advocacy at all.
This also gives me an excellent opportunity to link again to Keith Hennessey's wonderful description of exactly what everyone involved in White House economic policy actually does. I suppose I should also link to Bruce Bartlett's dissenting view (he thinks the NEC is a bad idea) and, why not -- to my defense of the NEC.
I'll also add a link to Andrew Samwick's endorsement of former Xerox CEO Ann Mulcahy to succeed Summers. While I continue to think it would be incredibly foolish to select someone for this key job based on how it would look -- the choice should instead be based on who would do the job well -- it is of course possible that Barack Obama and Rahm Emanuel believe that Mulcahy's management skills make her the best possible choice, and the public justifications (at least based on press reports) about what the business community will think are just spin. Nothing wrong with that. However, I continue to think that White House and government experience is more important for success in this job than is general (corporate) executive skill. If they like Mulcahy, I'd suggest Treasury Secretary for her, if that job is opening up soon.