I'm afraid it's hopelessly muddled. Josh Patashnik does his best here to rebut Ramesh Ponnuru's assertion that "the only way to square [Obama's positions on same-sex marriage] would be for Obama to say that he opposes same-sex marriage as a religious or moral matter, but supports it as public policy. He is, that is, 'personally opposed.'" But it's a strain. Dale Carpenter adds:
Assuming that Obama's opposition to gay marriage is not simply "personal," but is also a matter of public policy, I find Obama's current position perplexing. He opposes a referendum that would simply enshrine his purported public-policy view that marriage is between a man and a woman because, he says, it is "discriminatory."
But how is the proposed amendment any more "discriminatory" than his own position? His position is that marriage is between a man and woman; the proposed amendment says that marriage is "between a man and a woman."
I think the only plausible explanation is that Obama supports marriage equality but has decided not to say so for purely political reasons. Even his own ex-church supports it, for goodness' sake. For the record, this isn't a new position, tacking to the center. He has long held this incoherent position. And Obama knows what coherence is.