A lot of people have been making a lot of the fact that Obama didn't say the exact oath required by the Constitution until last night. I've heard several constitutional scholars on NPR saying this was nonsense, because the Constitution is clear that the term of the new President starts at noon on January 20, and it doesn't matter if the oath is said at all. My understanding, given that, was that the oath was constitutionally required but not a condition of the presidency beginning. It was just something Obama needed to do, just as the VP is constitutionally obligated to break tie votes in the Senate, and even if he did it late he did it. But his term starts before the oath in any case.
[Update: See comments.] Then I went and actually read the relevant portions of the Constitution.
I'm not sure it's all that clear who was president between noon on Tuesday and last night when he said the oath properly. I'm not saying that he wasn't president, but it's not clear if he was or in what sense he was if he was, and it's not clear if anyone was legally allowed carry out the duties of the President. Here are the relevant stipulations in the Constitution:
1. The previous president's term ends on Jan 20 at noon.
There's no indication in that amendment about the next president's term beginning at that time, despite claims by several constitutional scholars I heard on NPR that it does say such a thing. So Bush was clearly no longer President, but that amendment says nothing about who, if anyone, was.
2. Article 2 does specify the oath to be said. It says the new President must say it "Before he enter on the Execution of his Office". It seems pretty clear that Obama couldn't enter on the execution of his office, whatever that means, until he said the oath or affirmation that follows (I believe to accommodate Quakers, it gives the option of swearing the oath or simply affirming it). So he was violating the Constitution if he was executing his office before Wednesday night if the oath he said isn't the same oath the Constitution requires.
3. Article 2 goes on to say: "In Case of the Removal of the President from Office, or of his Death, Resignation, or Inability to discharge the Powers and Duties of the said Office, the same shall devolve on the Vice President, and the Congress may by Law provide for the Case of Removal, Death, Resignation or Inability, both of the President and Vice President, declaring what Officer shall then act as President, and such Officer shall act accordingly, until the Disability be removed, or a President shall be elected."
It's not entirely clear to me if the last clause "until the Disability be removed, or a President shall be elected" applies grammatically only to the bit about someone provided for by law (or in the actual case an amendment providing the line of succession declaring it to be the Speaker of the House) or if it also applies to the first part about the Vice President. I first thought the latter, since otherwise the election of a president doesn't remove the vice president from office when it would remove someone lower in the line of succession. That would be weird, and I can't see how the wording could have intentionally meant that. So that looks like any vacancy or inability of the president to perform duties (such as Obama being constitutionally prohibited from entering the execution of his office) would make the VP President or someone down the line of succession if there is no VP. But it could be the former, if there's a need to fill the gap with no elected officer to step in, and the former case is when an elected VP can take over, and there's no need for an election to fill the gap.
Biden had already been sworn in by noon on Tuesday, so presumably he was VP already at noon. I don't see any argument that he couldn't have been VP just because Obama hasn't sworn the oath, and this would be true even during the short intervening time between noon and an oath normally taken in the proper way just afterward. So on the assumption that an inability to enter into the execution of his office means he was not yet President, I think there's an argument that Biden was at least acting President, then, if Obama was not President. I don't think there's any reason to think Pelosi was, as some have claimed, and it's certainly not possible that it was Bush or Cheney. I think there's even an argument that Biden was acting President if Obama was President but couldn't carry out his duties as President because he hadn't entered the execution of his office. [But this may not be so if he hadn't said the Presidential oath, in which case no one could act as President. He had said the VP oath, but that probably isn't sufficient.]
4. But there's even one more puzzling factor. The article 2 paragraph I quoted does have that bit at the end "until the Disability be removed, or a President shall be elected." The Disability was clearly removed when they did the oath properly last night, so there's no question that Obama is now President in every important sense. But on the assumption that he wasn't President when he didn't get the oath right, there's still the election to account for if the last clause applies to the whole sentence and not just the case of a line of succession below VP. The condition says "or a President shall be elected". A President was elected by that point. What does that mean? Is it an argument that Obama really was President, even if Biden was Acting President?
There are several steps in this are unclear enough to me that I wouldn't be very sure about them, but there's a plausible case for that, unless Biden would have had to say the oath himself intending it to be for the acting presidency, in which case no one was acting as President in the intervening time. The line of succession specifies who takes on the Presidency in the event of a vacancy or inability to perform the duties. But it doesn't say they immediately become President. In fact, Pelosi would have to resign from the House to become Acting President, which she would never do for a temporary lapse because then she couldn't return to her House position as a Representative (although the House could re-elect her as Speaker even if she's not a member of the House, as far as I can tell; they've just never done that). The same would be true of Senator Bird, who is next in line, with his Senate seat, except that he could be reappointed to the Senate by his governor (although I believe he'd lose his seniority because of a gap in service and thus lose his status as President Pro Tempore). There's no condition of resigning from a cabinet position, though, and there's no specification that cabinet positions end at noon on Tuesday. In fact, some departments are now actingly-headed by Bush appointees who didn't resign, since a number Obama's appointees have not yet been confirmed. So presumably Condoleeza Rice, if she'd taken the oath to be Acting President, could have been Acting President given that Obama and Biden hadn't taken the Presidential oath and that Pelosi and Bird hadn't resigned from Congress. There's never any way such a thing would happen when none of the people higher in the line of succession were dead or incapacitated in any way but due to technical legalities, but I think that's the legal possibility.
It's funny how an argument that I thought was crazy after listening to some pretty confident constitutional scholars actually appears to have some merit, but I'm very hesitant to take it as far as many have and say that Obama wasn't President in any sense in that intervening time. I do hope he redoes anything he signed during that time if he wants to make sure they are legal (although some of them I'd probably be happier for them not to be law, so maybe I should be careful what I wish for).