The founders sought to provide via the Constitution a protection against an Obama, someone whose loyalties were lodged elsewhere. However, they did not contemplate that society would evolve from a royalty based loyalty to a ideology based loyalty. Therefore we find no such language in the Constitution and our belief that the natural born citizen clause defends us against traitors is but a chimera.
It would have defended us against trash like Obama but for the tampering to the meaning which has been perpetrated since the 18th century.
Under the original meaning, Obama would be a Kenyan, not an American.