Howard Wasserman asks the question. I haven't looked closely at the issue, but I would think the answer is that Obama was President at noon under Section 1 of the 20th Amendment:

The terms of the President and Vice President shall end at noon on the 20th day of January, and the terms of Senators and Representatives at noon on the 3d day of January, of the years in which such terms would have ended if this article had not been ratified; and the terms of their successors shall then begin.

  It is true that Article II, Section 1 states the following:

Before he enter on the execution of his office, he shall take the following oath or affirmation:--"I do solemnly swear (or affirm) that I will faithfully execute the office of President of the United States, and will to the best of my ability, preserve, protect and defend the Constitution of the United States."

  The question is, does Article II, Section 1 impose a condition on becoming President, or is it a constitutional duty that a person who has already become President must satisfy before he exercizes the executive power? Put another way, is a President who has not yet taken the oath still "the President," or is he just some guy who will become the President when he takes the oath?

  As a textual matter, I would think that the President who has not yet taken the oath is still the President. In particular, Article II, Section 1 refers to taking an oath before entering "the execution of his office," suggesting that the office of the Presidency is already his before the oath is taken. And the text of the 20th Amendment is unusually precise about the timing: At noon, "the terms of their successors shall then begin." If the new Presidency began when the oath was taken, I would think that the 20th Amendment would say that. So it looks to me that Obama became the President at noon, and that he was supposed to (and did) take the oath before exercising his executive duties, in this case at 12:10. That's my initial sense of it, at least.