I strongly recommend Jonathan Chait's largely pessimistic view (from the point of view of those who want legislation) of the chances of getting anything restricting guns in any way whatsoever through the House. And if that's correct -- if conservative Republicans remain dead set against anything at all -- then there's almost nothing Barack Obama can do about it (see, too, David Frum's view, which points out the possibility that presidential public leadership could easily polarize the debate and therefore backfire).
That said: I wouldn't completely rule out the possibility that legislation of some sort could be passed, and the president does in fact have a role to play in that. Obama should certainly be actively sounding out Republican leaders to see if there's a deal that could be done, either at the beginning of the next Congress or even during the lame duck session. Is it likely that Republicans would be willing to pass something? No. Is it impossible? No, it isn't, and if they're willing, Democratic leaders in Congress and the president should aggressively seek out any areas of agreement that might exist and try to get it done.
If there really is a deal out there, I'd guess that it would have to be done as far from the cameras as possible -- or, at least, it would be done as far from the cameras as Republicans think would help them. Yup, that's right: if something is going to pass, Republicans get an enormous amount of leverage over what it is, how it's written, and how it's presented publicly. Because without them, you have nothing. Obviously, the president and Democrats won't sign on to anything they believe is counterproductive, but among the wide range of items that gun control advocates think might do some good, it's pretty much up to Republicans -- House Republicans, really -- to pick which ones they can accept. Not only that, but if Republicans demand some (believed by gun control advocates to be) counterproductive items as part of an overall bill, they'll almost certainly get them as long as the bill, overall, is better than the status quo.
The president could give every eloquent speech in the book, but it won't make any difference in the short term. There will be a bill if and only if Republicans want one, and if that's the case they'll pretty much have all the leverage as to what's in it. The only things Obama and the Democrats can do is to make it as easy as possible for Republicans to sign on, and to use their legislative and substantive expertise to make sure the bill does everything Republicans would allow it to do. Those are important things!
Of course, the answer might well be that there is no give here; there may be no possible legislation that can pass the House that Barack Obama would sign. If that's the case, then federal legislation for at least the next two years, and most likely at least the next four years, is impossible, and those who want action need to think about what a long-term campaign should look like. Indeed: even if something can pass, the next step would have to require a long-term plan. Would the best strategy focus on the states? The courts? The Democratic Party -- and if so, the presidential campaign, or downballot primaries? General elections? Popular opinion, saving any active legislative campaign the future? Other options? That's a tough question. And even if something can pass now, it's not going to be much, and that means that the "what next?" question will still need to be asked.
As always, two contradictory things about the American political system dictate all this: on the one hand, veto points are real and often simply cannot be overcome, but on the other hand, the political system really is open to democratic political action, as difficult as that may be. The trick is to accept the reality of the limitations of the system without just giving up, since the opportunities for relatively small groups to influence things is real, too.