Probably not until his miserable butt is voted out of office or impeached and probably not even then.
As others have said, he need merely only present proof of the fact that he was BORN an American citizen and the issue would evaporate. But even then, if some people questioned the proof, SO WHAT? In a Republic and a democracy people can say whatever they want about politics even if evidence to the contrary is presented.
Did this guy study constitutional law in Cuba under Castro??
You see this thread?
The proof we are seeking would be proof he is a NATURAL BORN Amercan citizen. Arnold is an American citizen, but is not constitutionally qualified to serve as POTUS.
If he could or did present said proof, then it would also prove he is a liar and a fraud, as his father could not be BHO, Sr. if he is indeed a natural born American citizen.