That's going too far. If he was born in the United States, he gets 14th amendment citizenship. (Not the same thing as "natural citizenship because it was created by an act of Congress.)
Only if he was born outside of the United States would he not be an American citizen at all. There is a little evidence that indicates he might have been born in Canada, but mostly it is just circumstantial, nothing conclusive.
Based on what? He doesn't meet the "subject to the jurisdiction" requirement defined by Judiciary Committee Chairman Trumbull in the Congressional Globe (Record):
"The provision is, that ‘all persons born in the United States, and subject to the jurisdiction thereof, are citizens.’ That means ‘subject to the complete jurisdiction thereof.’ What do we mean by ‘complete jurisdiction thereof?’ Not owing allegiance to anybody else. That is what it means."Obama was born a Brit, thereby owing allegiance to a foreign power at birth.
The DNC has already publicly admitted that British Nationality Act of 1948 governed Obama's status at birth.