Congress has Constitutional authority over naturalization and immigration laws. The existing law is that a natural born citizen is someone who was a citizen at birth, and a person is a US citizen at birth if they have at least 1 American birth parent, regardless of the actual location of birth.
The citizenship status of Obama's mother is unquestioned. Thus, he is a natural born American citizen. Period.
I think Obama falls under the last one:
Under Title 8 of the US Code, Section 1401 defines the following as citizens of the United States upon birth
or natural born citizens:
Anyone born inside the United States. The person must be subject to the jurisdiction of the United States. (This would exempt the child of a diplomat, for example, from this provision.)
Any Indian or Eskimo born in the United States, provided being a citizen of the U.S. does not impair the persons status as a citizen of the tribe
Any one born outside the United States, both of whose parents are citizens of the U.S., as long as one parent has lived in the U.S.
Any one born outside the United States, if one parent is a citizen and lived in the U.S. for at least one year and the other parent is a U.S. national
Any one born in a U.S. possession, if one parent is a citizen and lived in the U.S. for at least one year
Any one found in the U.S. under the age of five, whose parentage cannot be determined, as long as proof of non-citizenship is not provided by age 21
Any one born outside the United States, if one parent is an alien and as long as the other parent is a citizen of the U.S. who lived in the U.S. for at least five years (with military and diplomatic service included in this time)
I think the law is stupid. If the people want to elect someone, that is the will of the people. It shouldn't matter where they were born or who their parents are.