"The speaker told the president that if the Senate amends the House-passed legislation and sends back a plan, the House will consider it - either by accepting or amending," a GOP aide close to the negotiations said. "The group agreed that the next step should be the Senate taking bipartisan action."
After leaving the Oval Office, the Senate Democratic and Republican leaders announced on the Senate floor that they're aiming to have a proposal on the fiscal cliff drawn up by Sunday, with the potential to put it on the Senate floor that afternoon.
"We had a good meeting down at the White House," Sen. Mitch McConnell, R-Ky., said. "We are engaged in discussions, the majority leader, myself and the White House in the hopes that we can come forward as early as Sunday and have a recommendation that I can make to my conference and the majority leader can make to his conference."
McConnell said that he is "hopeful and optimistic" and they'll be "working hard" over the next 24 hours "to see if we can get there."
Majority Leader Harry Reid, D-Nev., echoed those sentiments.
"We certainly hope something will come from that," Reid said of today's White House meeting. "The Republican leader and I and our staffs are working to see what we can come up with. We shouldn't take a long time to do that."
The Senate will come in at 1 p.m. on Sunday. There will be a caucus meeting in the afternoon. Reid says he hopes by that time on Sunday there will be a determination if a proposal can be brought to the floor.
"There was not a lot of hilarity in the meeting. Everyone knows how important it is, it was a very serious meeting," Reid said on today's White House meeting.
Reid warned that whatever they come up with it will be "imperfect."
"Some people aren't going to like it," Reid said. "Some people will like it less but that's where we are. And I feel confident that we have an obligation to do the best we can, and that was made very clear at the White House."
Despite the small hope, the prospect remains that any hypothetical agreement would only be a temporary-stop gap measure. Earlier today Senate Republicans are mourned the prospect of such a small deal to solve the immediate fiscal cliff problems today because they say a half-measure would leave the bigger issues, like entitlement reform, without a solution for reform.
"It's pretty apparent that we're not going to do what we've been called to do," Sen. Bob Corker, R-Tenn., said at a press conference before the leadership summit. "Without anything that is bold in place that's probably not going to happen." Corker predicted some sort of scaled-back short-term measure will be passed and that it will show the lack of "courage" of the president.
"What's likely to happen at the end of this year is we're going to end up with a small, kick-the-can down the road bill that creates another fiscal cliff to deal with this fiscal cliff. How irresponsible."