Where someone is born just isn't a very telling biographical fact.
Obama has released his long-form birth certificate now, and the skeptics are trying to make sense of the news and finding new objects of suspicion. Donald Trump, after congratulating himself for the whole thing, acknowledged that, "It is rather amazing that all of a sudden it materializes." Do you guys want his birth certificate or not?
But why do we even care whether Obama—or any president—was born in the United States? Section 1 of Article Two of the Constitution states that "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." Let's just get rid of that requirement.
Presumably, the rationale for the Natural Born Citizen Clause is to exclude candidates who have an allegiance to another country. But whether someone is born in the United States isn't a perfect predictor of whether they have America's interests at heart. We have characters like John Walker Lindh and Timothy McVeigh—born in America and working hard to destroy it—and also immigrants like Arnold Schwarzenegger and Sergey Brin—born elsewhere but devoted to their adoptive country.
In trying to decide who's "American enough" to be president we don't need a rule about where candidates are born, anyway. Looking at the candidates themselves is far more valuable than looking at their birth certificates. That's exactly what the voters do now, and they'd keep doing it if we cut the Natural Born Citizen Clause. Candidates who aren't pretty obviously American would get scrutinized—and eliminated from the race—by the democratic process. It's not as if a bureaucrat from Communist China would fly over from Beijing and somehow slip through the cracks to become commander in chief.
Where someone is born just isn't a very telling biographical fact. It is, after all, something one has no control over. Obama was actually born in Kenya? Great! What do his decisions since being born tell us about which country's interests he cares most about?