Seriously, what do they think him being non-American is going to change? Whether Obama is Kenyan or Hawaiian or Martian, he's still OBAMA. He's still got all the positives and negatives that he always had. Where he is from is irrelevant, especially now that his term is almost over. God this is a waste of time.
If he were not a natural born American citizen (which he is), it would not be legal for him to be president.
US Constitution Article II Section 1:
http://www.usconstitution.net/const.html#A2Sec1
No person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty-five Years, and been fourteen Years a Resident within the United States.
Presumably, therefore everything he has done as president: laws he's signed, law's he's vetoed, judges he's appointed etc would be null and void. Since the matter has never been adjudicated it would be up to the Supreme Court to decide the consequences of determining that a sitting president was unqualified for the office.
Truth to tell, however, I don't think much of this has to do with legality. I think it's cognitive dissonance. To a lot of Birthers it seems to be an impossibility that such a person (hint: race) could be president, therefore there must be some reason why he really isn't.
People get very strange when their underlying presumptions are challenged by reality.