The US Supreme Court would probably not accept such a case, and Obama will probably never get a chance to change the balance of the Court, unless Justice Kennedy retires. Obama will more likely get a chance to replace Ginsburg and Stevens, who are the most liberal justices.
It is interesting that the challengers of the proposition may have a point. Same-sex marriage has been considered a fundamental right in California. That is what the controversy is all about. If California law requires that amendments affecting a fundamental right must first be approved by the legislature before going to the general public, then the proposition could be invalidated by the California SC. I was unaware that this was a possibility, but it would be very good news if it is true. The whole purpose of such a requirement would be to protect the rights of minorities against attempts by a majority to suppress them. For example, one apparently cannot float a proposition in California to restrict the use of certain public drinking fountains to whites only. Such an amendment would be invalidated by the US Supreme Court, as well, but marriage laws are considered matters governed by state law.
My own position on this is strictly libertarian. That is, I think that the government should regulate civil unions, because civil unions are legal contracts that affect the rights of others. Marriage, on the other hand, is not something that the government should have anything to do with. Let churches establish their own doctrines on what constitutes a marriage consistent with religious doctrines. Let them conduct marriage ceremonies according to their own principles. Let others, including gays, define marriage as they see fit. Get the government out of the bedroom and out of consensual relationships. Governments are necessary to define and enforce contractual arrangements. They are not necessary to define and enforce personal relationships.