Various folks are trying to sort out just what Obama means with this statement:

That’s why I think it’s very important for us to have a methodical, open process over the next several weeks and then let’s go ahead and make a decision. And it may be that if Congress decides, if Congress decides we’re not going to do it, even after all the facts are laid out, all the options are clear, then the American people can make a judgment as to whether this Congress has done the right thing for them or not. And that’s how democracy works, and there will be elections coming up and they will be able to make a determination and register their concerns one way or another during election time.

I think it’s pretty damned clear, actually. After all, he had just said this:

What I’d like to do is have a meeting whereby I’m sitting with the Republicans, sitting with the Democrats, sitting with health care experts, and let’s just go through these bills – their ideas, our ideas – let’s walk through them in a methodical way so that the American people can see and compare what makes the most sense.

So then, following “President’s Questions” and the GOP’s performance at same, Obama feels he (and, by extension, his party) is/are the ones with the real solutions (as opposed to mere slogans), no matter how flawed those solutions may be, to the truly existential problems facing our government. The GOP, on the other hand, is suggesting we can simply cover everyone, lower taxes, and still have budget surpluses to use on all the wars we can start as far as the eye can see.
In fact, the only member of the GOP caucus putting real ideas out there that could do anything about the situation at hand is Paul Ryan ® of Wisconsin, who comes right out and admits that:

Just look at the numbers. [That the healthcare problem is the deficit problem is] not a theory. It’s a fact.

-and that-

if Ron Wyden and I were in a room, we could hammer out a deal [merging our healthcare proposals] by tomorrow.

And but Ryan basically wants to cap Medicare benefits, privatize at least parts of Social Security, and a do whole host of other stuff that I’d disagree with. That’s not important, though. The point is: these would be extremely unpopular positions to put into law, but at least they are positions. They are not sound-good, rhyming boilerplate nonsense; they are actionable “solutions” that could be turned into actual legislation that might do something about the problem (again, this is whether you agree with the particular mode of the solution or not). This is radically different from what the rest of his caucus proposes, which can be efficiently boiled down to “USA! USA! USA!”

So then, what Obama is saying is this:

Let’s get the key, decision-making personnel and folks with real ideas in a room, Democrats and Republicans. We’ll have all the plans and ideas, the GOP will have nothing to offer other than elimination of extremely popular programs, assuming they even offer that. Even if a deal doesn’t get done, there are clear positions taken, clear stances made public in a way that can’t be taken back, and is ultimately very similar to what the “Questions” televent did. It will be live, and it will be compelling. As such, any deal that actually comes out of it basically has to pass, otherwise the GOP look like the two-faced negotiators that they have proven to be (but have yet to be called out on). Failure to make a deal most likely also redounds on the GOP, since they would ideally be seen as having no ideas to offer anyway (assuming they just show up and scream platitudes while the Democrats actually have functional legislation and CBO scoring to offer). Thus, you show America in microcosm (and, not coincidentally, in TV drama form) the real reason “nothing gets done” in D.C. and, simultaneously, make the GOP look very small indeed. Or you get a healthcare deal.

The key to this plan, though, is the CBO (or whoever could reasonably play Ref in this debate). You can’t just run the numbers in 48 seconds and, on the spot, call out somebody’s plan as totally unworkable horseshit. So the more likely outcome of such an event would be a draw; two weeks later, nobody bothers to check that the GOP “plan” consisting of rhyming maxims and hoary chestnuts about using the ER as your PCP scores poorly (if at all), while the Democratic plan of actionable legislation scores as a deficit reducer and, oh by the way, covers 30 million presently un-covered Americans out of the gate. And such an outcome redounds to the generally negative perception of the Democrat as a feckless, do-nothing, non-governing, circular firing squad failure machine. So, I guess this is pretty much what’s going to happen. Whatever it is, it’s always good for the Republicans.

You heard it here first.