Now I may be no extreme fan of Obama but here is what I found on citizenship,
Through birth abroad to two United States citizens
See also: jus sanguinis
A child is automatically granted citizenship in the following cases:
1. Both parents were U.S. citizens at the time of the child's birth
2. At least one parent lived in the United States prior to the child's birth.
INA 301(c) and INA 301(a)(3) state, "and please one of whom has had a residence." The FAM (Foreign Affairs Manual) states "no amount of time specified."
A person's record of birth abroad, if registered with a U.S. consulate or embassy, is proof of citizenship. They may also apply for a passport or a Certificate of Citizenship to have their citizenship recognized
http://en.wikipedia.org/wiki/United_States_nationality_law