If Obama was born in Kenya, then his mother couldn’t have conferred citizenship on him. The law said that you have to be a citizen for 10 years with at least 5 of those years being after the age of 14. Obama’s mother was 18 when she gave birth, so she did not meet the requirements to confer citizenship on him.
The issue seems to be debatable but certainly doesn’t seem to be the open-and-shut case as many think it is. If a U.S. soldier marries overseas and has a child, that child should be a natural-born citizen at birth.