Many of the people who think Obama wasn't born in the USA may not even realize that that would have some bearing on his eligibility to be president. They may like Obama, think his presidency is legitimate and legal, but they're just repeating some fragment of a rumor they've heard somewhere about where he was born. I think the %age of Americans who know about the "natural born citizen" rule is far lower than you may think.
Heck, according to this:
http://publicpolicypolling.blogspot.com/2009/08/deeper-look-at-birthers.htmlsome of these people correctly think he was born in Hawaii, but don't realize that Hawaii is part of the United States.