As has been documented many times on this site. BHO’s mother was too young to pass citizenship on to lil’ Barry according to the Nationality Act of 1952. We didn’t start doing the anchor baby crap until 1986.
That only applies if he was born outside the country. The Anchor baby thing goes back to the 14th amendment, and in the courts to Perkins v. Elg (1939) and Wong Kim Ark (1897), among others.
However neither case delt, directly at least, with the meaning of Natural Born Citizen. "Wong", whose parents were legal resident aliens, but still Chinese nationals, actually indicates that while they have same rights, there is a distinction between "natural born child of a citizen" and the "child of an alien, if born in the country". Both are just as much citizens, with the same rights, but there is a distinction. (Eligibility to the office of President is not a right, otherwise naturalized citizens would have it as well).
Elg was not actually an "anchor baby", she was declared, by the lower court, to be a "natural born citizen" and the Supreme Court agreed, but both her parents were naturalized US citizens at the time of her birth. (they later renoucned that citizenship and took her to Sweden, but that did not change her status as a citizen).