I think Obama is just following the instincts that got him elected. I read a story on Slate that explains how PE Obama tapped into people's emotional responses:
Obama in your Heart

The key to influencing people is not so much what you said, but rather how you made them feel. Nobody will remember Warren's prayer during the inauguration, but plenty of Evangelical Christians will remember how it made them feel to see one of their own up there with President Obama. I think we will see Obama's approval rating jump because many E.C.s will stop fearing him.

But now let's segue back onto the thread topic: I think that inducing these same types of feelings will be the key to acceptance of same-sex marriage. It may be lot's of fun to march in a parade with groups of guy's wearing jock straps or leather chaps, with a giant penis float. (And I have nothing aginst celibrating your sexual identity!) But scenes of those events on TV only induce fear in the hearts of Gay Marriage opponents.

If instead LGBT people (and their friends to a lesser extent) can reach out to those who fear them, and help them see that "they are just like me", and deserving of all of life's joys, then we might get somewhere. This approach has certainly worked for some politicians who have reversed their positions after learning that a loved one is gay or lesbian.

I know it's difficult to reach out to your enemies, but that's the only way to turn them into friends.