Some in Congress have been quietly working...
on trying to get the Constitution amended on that issue - to allow naturalized citizens, like Schwarzenegger, to become president. I believe it's been proposed every year since he became governor, but, not enough support to get to vote, yet. Might get less support in congress, however, after this next election depending on how things go.
I still like that line in the movie Demolition Man about the Schwarzenegger Library and then Sandra Bullock refers to changing the constitution before he became president.