Excepting diplomats, there is no mechanism to naturalize a person born in this country. The State Department has no such form. It cannot be done. There is no entry for citizenship of parent at the time of birth on any long form birth certificate. There is no separate identifier for natural born citizen on the U.S. passport. There is absolutely NO LEGAL STANDING for the birther position. Even if there were a historical leg to stand on it cannot be legally upheld in court today because it cannot be equally applied to all children since there has been no tracking of the citizenship of parents for the lifetime of anyone alive today. And that doesn't even take into consideration the equal protection rights of children who have no ability to track the citizenship of their unknown father.
To put it simply, the birther argument is made up, aka make-believe.
If you are going to argue the “natural born Citizen” issue, it would be appreciated if you can rely upon historical and legal sources rather than on your own personal opinion about what the world should be.