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The person having the greatest number of votes for President, shall be the President...

But the person in question must have first met the Article II sec. 1 clause 5 conditions for eligibility for the office.

"No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States."

But the person in question must have first met the Article II sec. 1 clause 5 conditions for eligibility for the office.

It says right there in black and white, whoever has the most votes for President shall be the President.

Any issues with regard to eligibility were clearly left to the political process. That that process may not have done as thorough a job as you would have liked doesn't change the fact that Obama is President and to date, no constitutional authority has deemed otherwise.