I honestly don't really think Obama gives a shit.
I mean, to start with, the guy doesn't really have any principles or anything he cares about other than himself. He (like many politicians) takes positions on issues based on what he thinks people want and what will get him votes and what sounds good in a speech, and he's is entirely a political creature.
So I think that because there isn't really much interest in the country for increased gun control, and because a lot of Dems in the House don't have much appetite for it, he doesn't really give a shit what the far left wing in his party thinks. He used those suckers to get elected, but he's got no loyalty to them at all.
Unless there's some GIANT rash of school shootings with black rifles, or something like tha, or Reid loses his re-election and we get Chuck Schumer as Senate leader, I don't think we'll see any serious push for gun control during Obama's next two years.