(Read more: Forget tapering, here's the really big Fed deal)
Chairman Ben Bernanke's term expires early next year, coinciding with multiple FOMC vacancies.
Five of the seven governor seats conceivably could be vacant on the 12-member committee, which fills the other five positions on a rotating basis with regional Fed presidents.
Along with Bernanke leaving, Sarah Bloom Raskin has been nominated as deputy Treasury secretary, Elizabeth Duke resigned in August, and the interim term to which Jerome Powell had been appointed expires Jan. 14. Speculation has been that if Fed Vice Chairwoman Janet Yellen doesn't get the top position, she will retire.
That leaves Obama in an extraordinary position in terms of potential Fed influence, given that the terms last 14 years.
(Read more: Upbeat Fed outlook suggests QE tapering is near
The political calculations are numerous, with some speculating that Obama may have tried a little reverse psychology by floating Summers' name, in hopes of slipping in a more viable name after an expected Summers uproar.
Market veteran Art Cashin, the director of floor operations at UBS, has been watching the situation closely and summed it up in his morning note Monday:
Had the president raised the name of the brilliant but controversial Mr. Summers to purposely inspire backlash in order to turn the Yellen candidacy from an appointment to an anointment? Yet, Mr. Summers' name surfaced again and again, with leaks from supposedly knowledgeable sources, who claimed to have heard he was the White House choice. That persistence led folks to wonder if Summers might be the first step to "stacking" the Fed.
The calculus could get tricky from here, Cashin said:
Will the president appoint Yellen? Some think he's bristling that Congress seems to be forcing the appointment rather than approving it. Who he nominates may tell whether there is an intent to reshape the Fed ideologically.
Traders rejoiced Monday, reasoning that Yellen would be less likely to stop the party on Wall Street.
The Bernanke Fed has acquiesced to market demands repeatedly, providing more than $2.6 trillion of liquidity throughout the major average's surge of nearly 150 percent since the March 2009 lows.
(Read more: Three reasons why the Fed should taper)
In coming months, the central bank is expected to begin decreasing its monthly purchase of $85 billion in bonds, and the market seems to believe that Yellen will take a more cautious approach than Summers would have.
That could be a mistake, Jessica Hinds, economist with Capital Economics, said in a note:
We do not think that the Fed's policy stance is likely to change significantly as a result of a new chair being elected, whoever is appointed. We're not convinced that Yellen, if she is selected, will take a much more dovish approach than Summers might have done.
Conservatives, meanwhile, are considering this a significant victory, even though key Republicans also opposed Summers.
They already were preparing their debt-ceiling strategy, with expectations for concessions over the Obamacare national health insurance plan, according to the Hill.
As a whole, the Summers defeat actually could mean a backstep for the president in terms of keeping the Fed on its easy money track, something the markets may find somewhat less pleasant in the long run.
—By CNBC's Jeff Cox. Follow him
@JeffCoxCNBCcom on Twitter.