The half-day meeting will take place on 25 February, after a congressional break between 15 to 19 February.
The move comes after complaints that Mr Obama's efforts have been too partisan and secretive.
Republicans welcomed the debate, but suggested that the only way to reach agreement would be to scrap the existing bill.
The logic behind this move is strange at best. The hope of getting serious bipartisan support is basically zero. It would seem the only chance, and a very tiny on at that, for Obama to get real Republican buy-in would be for him to offer up a radically different bill, but that is off the table.
When asked by Ms. Couric if he would agree to discard the bill and start over, the president said he would not. The starting point, aides said, would be with the proposals that passed the House and Senate.
What is the point of a meeting that is unlikely to provide any real results? That is tough to say. The idea that Obama will get five Republicans votes in the Senate because he sat down with them and added a few of their small changes to the bill is absurd. Max Baucus already wasted three months trying to craft a bill that could get a large number of Senate Republican votes, and he failed.
Most likely, Obama is hoping to make it look like he tried really hard to be bipartisan, hoping to embarrass Republicans by pointing out how terrible their ideas on health care really are. For instance, Paul Ryan's proposal to privatize Medicare and just give old people vouchers to buy less and less private insurance each year is a terrible and frightening idea, and Democrats should make a better effort at publicizing it.
After a year of ineffectual governance, if Democrats hope to survive the midterm, they need to show that the insane ideas of the Republican party make them a completely unacceptable alternative. Having Obama always talk about the GOP's "good ideas" is not helping. Having Obama publicly tear apart Republican ideas on health care might.
It is possible that Obama is trying to create political cover for a purely partisan reconciliation measure. Either way, this bipartisan meeting is going to add weeks to the health care debate. Clearly, Democrats will not pass a bill before February 25th. It would now look like bad form if Democrats even start officially marking up a reconciliation sidecar bill in committee before February 25th. In light of this newest information, we should not expect a health care bill until March at the earliest.