I don't think Schwarzenegger personally cares whether or not same-sex marriage is legal in California. His chief of staff is a lesbian, and he equivocated earlier this year about whether he woud sign a same-sex marriage bill if it passed in the CA legislature.

The Calif. legislature did pass a bill legalizing same-sex marriage in 2005 (the only state legislature to do so) but Schwarzenegger vetoed it – almost certainly for political reasons. He didn't want to be embroiled in the referendum that would be sure to follow.