In a discussion on the Trinity, Trent Dougherty at Prosblogion rasies the question of whether President Bush is his own president. There's a sense in which Bush is the president of those who voted for him, i.e. they (at least at one point) identified with him as the person they wanted to be president. There's a broader sense in which he's the president of every U.S. citizen, i.e. he's the president who governs over them. That's the sense Trent has in mind. In that sense he is Ralph Nader's president as much as he is James Dobson's.
But is he his own president? Trent thinks yes, and I agree. Mike and Dale in the comments say no, and they offer two reasons. First, he can't pardon himself, which means he doesn't have that particular authority over himself. Second, he's not under his own authority, because as the top executive he's not under anyone's authority. I've adapted what follows from my comment on that post.
As for pardoning, there are lots of powers someone might have that are limited. The fact that he can't pardon himself isn't evidence that he's not his own president. He also can't appoint himself vice-president if the vice-president dies or resigns, but I don't see how being exempt or prohibited from being the recipient of a certain power of the president means he's not his own president. It just means he doesn't have a president who can do that one thing for him (e.g. pardoning him, appointing him vice-president, etc.). I don't have a president who could appoint me vice-president (I'm not old enough), and neither does my wife (she's a naturalized citizen), but it doesn't mean Bush isn't my president or hers. The same goes for residents of Texas who can't be appointed vice-president because that would mean the president and vice-president would be from the same state. It means there's a certain presidential power that we can't be beneficiaries of, not that he's not our president. Why, then, does the fact that he can't be the beneficiary of the pardon count as anything more than the limiting of a power? It doesn't mean he has no authority over himself.
Bush presumably did vote for himself for president, and therefore he presumably got the president he voted for. Thus he has the president representing him whom he wanted representing him. I think that's a good enough reason to consider him his own president.