If your mother is a citizen of the United States at the time of your birth, then YOU are a citizen of the United States at the time of your birth, regardless of WHERE that birth took place. As a U.S. citizen at the time of your birth, you are a NATURAL-BORN CITIZEN OF THE UNITED STATES (the term is meant in contrast to "naturalized citizen," which is a citizen of another country at birth who later *becomes* a U.S. citizen, or of course "noncitizen," which would be someone who never became a U.S. citizen). If a pregnant American woman is on vacation in England and gives birth, that child is still a natural-born citizen of the United States. Such an occurrence would never preclude that child's eventual eligibility to become president of the United States. That would be absurd!
Now as far as I'm concerned you can make all the arguments you want about Barack Obama, but the whole "birth certificate" controversy is stupidity at its finest.