This question, made famous during the Watergate hearings, seems to be the driving question these days, whether one is speaking of the clumsy rollout of the Affordable Care Act, the number of people in the independent insurance market who will in fact lose their coverage, or the NSA’s surveillance program. In Dana Milbank’s words (Washington Post):

It stretches credulity to think that the United States was spying on world leaders without the president’s knowledge, or that he was blissfully unaware of huge technical problems that threatened to undermine his main legislative achievement. But on issues including the IRS targeting flap and the Justice Department’s use of subpoenas against reporters, White House officials have frequently given a variation on this theme. Question: What did Obama know and when did he know it? Answer: Not much, and about a minute ago.

Milbank concludes:

On one level, it would be reassuring — and much more credible — if the White House admitted that Obama is more in the loop than he has let on. On another level, it would be disconcerting: Is it better that he didn’t know about his administration’s missteps — or that he knew about them and didn’t stop them?

Eugene Robinson (Washington Post) also finds the claims of ignorance difficult to accept, albeit with a somewhat more ominous alternative:

Either somebody’s lying or Obama needs to acknowledge that the NSA, in its quest for omniscience beyond anything Orwell could have imagined, is simply out of control.

Both could be true, of course. The growing scale and complexity of government creates enormous problems of oversight and political control. Even if a well-intentioned and moderately intelligent president attends national security briefings and takes copious notes, there are distinct limits to how much one can know and how effectively one can alter the course of the bureaucracy.