When sworn in, Jimmy Carter had to say, "I, James Earl Carter." Ronald Reagan never used his middle name on the campaign trail, but he also was sworn in as Ronald Wilson Reagan. The first Bush never used his two middle names (they come across kind of old school elitist), but he was sworn in as George Herbert Walker Bush. Bill Clinton? Sworn in as William Jefferson Clinton.
One other perhaps most telling example: as you may know, Harry S. Truman's middle initial didn't stand for anything: he had two close relatives with S-names (one was Shipp (or Shippe) the other was Solomon) so his parents gave him just the middle initial rather than favoring one or the other.
According to Wikipedia:
Truman's bare initial caused an unusual slip when he first became president and had to take the oath of office. At a meeting in the Cabinet Room, Chief Justice Harlan Stone began reading the oath by saying "I, Harry Shipp Truman, . . ." Truman responded: "I, Harry S. Truman, . . ."
What we can take from this is that the Chief Justice (or his clerks) had felt the need to research what Truman's middle initial stood for, and settled on Shipp, so that Truman would properly take the oath of office.
Now there is no direct requirement in the Constitution that a President must take the oath of office using his full name, but it seems to me there must be some law, regulation or perhaps Supreme Court rule that requires it. It is highly unlikely that the outgoing Bush administration will help Obama by changing this before January 20th (if Obama can somehow win in November.)
At the least, it seems that Barack Obama will have to be sworn in as Barack H. Obama, if not the full Barack Hussein Obama.