Obama is an unknown person and no one seems to care. I think the requirement is constitutional, so those who run for the Presidency, by constitution, must prove their natural born status.
To whom must they prove it?
Since it is Constitutional, and since the Chief Justice receives the oath of office, then I’d say it’s up to the Scotus to speak to the eligibility of anyone receiving that oath.
It must be the Scotus.
Here’s an interesting scenario. If Obama is ruled ineligible to be POTUS before he is given the oath of office, then I would suspect that the electors for Obama would be ruled ineligible and since McCain would not have enough electors to be elected on the first vote, then the election would fall into the house of representatives. If the election is dropped into the lap of the house of representatives, there is only one likely candidate to emerge as POTUS. And we all know who she is.