Neither was John Jay, but he wrote the letter to G. Washington that seems to have resulted in the term being included in the Constitution's eligibility clause. His concern? The influence of foreigners in the national government, particularly in the command of the national Army.
True enough, but I fail to see how this gives us any insight on what the term “natural born citizen” means.
Obama is not a foreign military officer.
His idea of what being an American means or should mean is quite different from mine, but there are a great many Americans, unfortunately, who agree with him, not me.