Bernstein does grant that "it's possible that when Obama re-appointed Bernanke he thought he had such assurances, and it's possible that he believed that Fed policy to that point combined with fiscal stimulus would be sufficient to beat the recession, so that he underestimated the importance of the Fed in getting the economy back up to speed." Finally, he arrives at what may have been the key point for Obama decision:
It's also fair to say that a year ago, in the wake of the financial crisis, reassuring the markets and keeping in place the person who had experience dealing with those issues was probably a more legitimate concern than it is today.
As is the case on so many fronts, Bill Clinton, facing a rejectionist Republican majority, worked under constraints similar to those confronting Obama (and if Republicans capture one or both chambers of Congress this November, as seems increasingly likely, the operating environment will be more similar still). According to Taylor Branch in The Clinton Tapes, when Clinton reappointed Greenspan in 1996, he
had wanted badly to replace chairman Alan Greenspan with Felix Rohatyn, the shrewd investment banker from Lazard Freres, but he ran into vexing constraints everywhere. Rohatyn himself advised Clinton to reappoint Greenspan instead, arguing that the Republican Senate would confirm no one else. Wall Street could not elect a U.S. president, Rohatyn told him, but it could surely un-elect one. If threatened, financial, financial powers would sacrifice short-term profits to drive interest rates higher, hurting blue-collar workers with layoffs and shaky pension funds. In the end, Rohatyn refused appointment to both posts -vice chair as well as chair], and Clinton suspected that Greenspan had engineered this result by warning of political friction and terrible drudgery at the Fed. He thought the wily incumbent protected his brittle ego from comparative scrutiny alongside Rohatyn, who was just as accomplished and a far more persuasive, attractive public speaker (p. 348).