Updated: 10:55 p.m.

Despite a flurry of high-level meetings and negotiations this weekend, by Sunday evening House and Senate leaders appeared no closer to a deal to raise the debt ceiling. Instead, both sides were pursuing separate proposals that they thought might be able to pass their respective chambers.

House GOP leaders were reluctant to offer details of a plan, even during a 4:30 p.m. conference call Sunday with Republican Members. The White House called Democratic leaders to a Sunday evening meeting for further talks.

Speaker John Boehner had said he wanted to show progress by Sunday afternoon, but the Ohio Republican failed to meet this goal even as he was continuing to discuss the matter with President Barack Obama and a bipartisan group of House and Senate leaders. Those talks came after the Speaker announced an impasse with the White House on Friday evening.

During the Sunday conference call, Boehner continued to combat mistrust in his Conference. He told his members: “There are no secret negotiations going on. So don’t worry. The path forward is not an agreement between me and the president. The path forward will be a measure that we can stick together on that can reach the president’s desk,” according to a source familiar with the call.

However, Boehner did acknowledge that the GOP’s Cut, Cap and Balance proposal was no longer valid because of Senate opposition, and he said the GOP needs to focus on “what can we pass to protect the country from what the president is trying to do,” according to the source.

Boehner appeared to be moving toward a proposal that would raise the debt limit in at least two stages, or tranches.

Senate Democratic aides indicated that Senate Majority Leader Harry Reid (D-Nev.) was preparing to move forward with a bill of his own to raise the debt limit and cut into the deficit, especially if Boehner follows through on his vow to model his plan after the Cut, Cap and Balance bill, which failed the Senate on Friday.

“There is a lot of theater going on at the moment as everyone says what they need to say before doing a deal,” one Senate aide said Sunday afternoon. “I don’t know what that deal will look like, but this all ends with a deal.”

However, the lack of agreement threatened to roil stock markets around the world Monday, and leaders at the outset of the weekend seemed to acknowledge they were scrambling to prevent a panic in trading, including in Asian markets that opened for Monday business on Sunday night.

Once it became clear that it would not be able to announce anything definitive, House leadership began to downplay the absence of a deal. Brad Dayspring, spokesman for House Majority Leader Eric Cantor (R-Va.), posted on Twitter Sunday afternoon: “Note: There are 9 days before Aug 2. For those talking about Asian Markets, would recommend not stoking fear/concern. Work is being done.”

Throughout the weekend, the president and his emissaries continued to say that he will not sign into law any legislation that does not extend the debt limit through the 2012 elections, and Republicans insisted that time had run out for that kind of deal to be done. With a little more than a week left, it appeared that raising the debt limit in stages over the next 17 months was emerging as a serious proposal on both sides of the Capitol. 

“I would prefer to have a bipartisan approach to solve this problem. If that is not possible, I and my Republican colleagues in the House are prepared to move on our own,” Boehner said on “Fox News Sunday.” “There will be a two-stage process; it’s just not physically possible to do all of this in one step.”

Boehner’s open endorsement of a two-step process is not new. According to Democratic sources, Reid came to a hastily scheduled Saturday evening meeting with Boehner and other leaders armed with a “range of proposals that encompassed the different ways of doing the two tranches,” a senior Senate Democratic aide said Sunday.

One of the main sticking points was what could be done legislatively to trigger a second phase of deficit reduction. The aide said Reid proposed several options, including using a joint budget “super committee” envisioned by Reid and Senate Minority Leader Mitch McConnell (R-Ky.) during discussions on McConnell’s now-obsolete Plan B proposal. That special panel would be able to force votes on their proposal on the floors of both chambers. A mechanism to instruct committees to take up some form of the “gang of six” deficit reduction framework was also discussed.

In an openly frustrated statement issued after Saturday’s meeting in the Capitol, Reid called out Boehner and McConnell.

“Their unwillingness to compromise is pushing us to the brink of a default on the full faith and credit of the United States,” Reid said. “We have run out of time for politics. Now is the time for cooperation.”

Behind the scenes, though, Reid has been working constantly with his Senate counterpart. The two even met at 3 p.m. Friday in McConnell’s office after receiving notification that Boehner would be walking away from the table again.

In addition, Obama met with Reid and House Minority Leader Nancy Pelosi (D-Calif.) on Sunday evening at the White House to discuss the situation.

Because any one Senator can delay action for days with an attempted filibuster, the time constraints faced by the Senate made Sunday night and this morning crucial for the chamber to settle on a procedural game plan.

“Under the best of circumstances, a controversial bill will take you a week to go through the Senate. And so we need to have an understanding today and move forward,” Senate Majority Whip Dick Durbin (D-Ill.) said Sunday.

Asked whether McConnell had reached out to more conservative Senators like Jim DeMint (R-S.C.), Rand Paul (R-Ky.) or Mike Lee (R-Utah) in an attempt to head off any potential filibusters, a Senate Republican leadership aide would only say that the leader has had several meetings with Members.

Following the White House meeting Sunday night, Reid announced that he was assembling a $2.7 trillion deficit reduction package. In a nod to Republicans, the measure would equal the size of a debt limit increase through the end of 2012 and would not include revenues, he said. He also accused Boehner of pursuing a short-term debt deal in disguise, which he said would be a non-starter for the Senate and the president.

In order to achieve the $2.7 trillion figure, it’s possible Democrats will factor in savings from projected wind-downs in the American missions in Afghanistan and Iraq, a source confirmed. Pelosi had mentioned using this sort of accounting in a luncheon question-and-answer session with progressive reporters earlier in the week. How much savings the Congressional Budget Office would calculate based on these assumptions, however, is in dispute.

A Hill Democratic source said pursuit of Reid’s $2.7 trillion plan “looks likely.”

But aides emphasized that although the offer creates another option as time runs out, it “does not foreclose the possibility of a two-step proposal.” They also suggested an openness to amending the proposal, such as adding a deficit reduction panel, if such tweaks could garner GOP votes.

A top aide said, “Any path forward on a two-step solution would require the Speaker to revisit our offers from last night, but based on estimates that have already been provided by the Congressional Budget Office, we’re confident we have a package that would provide [$2.7 trillion] in cuts.”

Sources close to the potential bill added that the CBO score was pegged mostly to similar provisions already considered by the nonpartisan panel.

Steven T. Dennis, Humberto Sanchez, Jessica Brady, Daniel Newhauser and David M. Drucker contributed to this report.

Editor’s Note:

This article updates the print version to include details of Senate Majority Leader Harry Reid’s new debt plan that he announced after a Sunday night White House meeting.