I agree with the...
The question is not for all but a very few people not one of whether Obama is a US Citizen but is he a "natural born citizen."
The Constitution was clear that citizens of the United States at the time of the adoption of the Constitution were eligible if they had been resident for 14 years, subsequent to that the "natural born" rule would take effect. That makes the comment about Martin van Buren completely irrelevant.
There are two types of citizenship. The first is being "natural born" and having citizenship at birth and the second is being a citizen as a result of naturalization. Under the Constitution Congress makes the rules for naturalization.
The status of being a "natural born' citizen has two components. First is being citizen by jus solis and not simply jus sanguinis. That means that you must be born on US soil, or under the native Sun. Some but not most claim that it means also having parents who are citizens, which is citizenship by the blood. Citizens born to US citizens outside of the country are considered as "naturalized at birth" by virtue of jus sanguinis, which is to say due to their parents blood.
In addition to the fact that "natural born" means that you have to be a citizen at birth and not by naturalization there is usually considered to be another restriction on being a "natural born" citizen. It is usually held that if a "natural born" citizen takes an oath of allegiance to any other sovereign then they give up that status. At some periods it has been held that doing so means renouncing your US citizenship and at other times the possibility of dual allegiance or citizenship has been admitted. If citizenship is lost then would have to be reapplied for but even if it is retained after acknowledging a foreign loyalty the status of being "natural born" would be lost and the person would be considered as simply being a citizen who was naturalized at birth, as if born overseas to a US citizen.
Now some people make an issue of Obama having been adopted by his Indonesian Stepfather and claim that makes him no longer a "natural born" citizen. That strikes me as untenable because it would give a noncitizen the power to remove US citizenship from a minor child. No US court would agree with such a position. What is more important would be if Obama had himself claimed to be a foreign national or taken some oath to a foreign sovereign after he became an adult.
That is why I would be more interested in seeing his travel records to find if he had traveled under the protection of a foreign passport after his 18th birthday. That could be disqualifying. In addition if he claimed to be a foreign national on his college financial aid forms then that would be likely to disqualify him. It would be likely to prove damning for several reasons. First because of the duplicity involved. Second because his doing so to take a financial benefit from the US taxpayer and then subsequently cover it up would be I think seen as repugnant even by many who supported him. That last is I believe the most likely case and I have always held that the birth certificate issue is likely to prove a red herring.
My expectation is that an examination of Barack Obama's birth records will show that he was born in the United States. Some have speculated that his father may be listed as UKN. That would prove embarrassing but would not in itself disqualify him from any office. If any wish to argue that being "natural born" means proving qualification under both jus solis and jus sanguinis, that is being born on US soil to US citizen parents, then that would be a new standard that has never been asserted and which no prior candidate was ever asked to offer proof of before. It has not been unusual until now for a successful politician to be a bit of a bastard.
Others have noted that his putative father was not only a foreign citizen, actually a subject of the British crown, here on a temporary student visa but that he himself would have been ineligible for an immigrant visa and Permanent Resident (Green Card) status or naturalization to become a citizen. That is because Mr Obama Sr. was a polygamist. That however would not be any bar to his child's citizenship or status at birth. It is likely that if he had not chosen to abandon his family he would have been allowed to gain a Green Card despite his polygamist past.
The question of why there is a special restriction on who is eligible for the office of President of the United States and whether it is wise or necessary is a political matter that is up to the people to determine. It can be changed by Amendment to the Constitution.