Updated: 7:30 p.m.

Senate Majority Leader Harry Reid (D-Nev.) signed off Sunday evening on a deal to avert a government default pending the approval of his Conference, adding that he hoped a vote could be held as early as late Sunday night.

Reid spokesman Adam Jentleson announced the Majority Leader’s support for a newly negotiated plan to raise the debt limit while enacting $3 trillion in deficit reduction after top Senate Democrats emerged from an hour and a half meeting with their House counterparts.

But sign-off from Senate leaders is just the beginning of what could be a tortuous process of getting the agreement to President Barack Obama’s desk. Speaker John Boehner (R-Ohio) and House Minority Leader Nancy Pelosi (D-Calif.) will need to wrangle their respective caucuses to reach the simple majority needed to approve the deal if it arrives from the Senate.

Rep. Chris Van Hollen, ranking member on the Budget Committee, said House Democrats are still looking at the details of the proposal. “A big issue is our Republican colleagues haven’t signed off on the deal, so let’s see whether they get there,” the Maryland Democrat said.

Emerging from a marathon round of meetings Sunday, Pelosi also kept quiet on whether she supports the framework. She will meet with the Democratic Caucus on Monday to discuss it. “We’ll all have to take a look. And we all may not be able to support it, or none of us will be able to support it, but we’ll wait and see, and we’re open to what comes down because, again, the stakes are very high here,” the California Democrat said.

House Members at the poles of the political spectrum have much to complain about in the pending deal and expressed their reservations as news of an agreement broke late Saturday and details trickled out.

Reid told reporters after the leaders’ meeting that he was hopeful that a vote could be held Sunday night, while his colleagues — Senate Majority Whip Dick Durbin (Ill.), Democratic Conference Vice Chairman Charles Schumer (N.Y.) and Conference Secretary Patty Murray (Wash.) — were otherwise tight-lipped as they exited Pelosi’s office suite.

The top Democratic leaders of both chambers had huddled to review an imminent deal with Republicans to raise the debt ceiling through the 2012 elections and slash $3 trillion from the deficit over the next 10 years. The first tranche would involve spending cuts worth an estimated $1.2 trillion, with the rest of the savings to be negotiated by a bipartisan joint Congressional committee charged with producing a plan by Thanksgiving.

The final sticking point had been the enforcement mechanism to pressure the panel into producing a framework for the extra $1.8 trillion in deficit reduction — or what Schumer referred to earlier Sunday as the “swords” hanging over the heads of both parties that will motivate lawmakers to reach an agreement this winter.

A preliminary outline between the White House and Republicans suggested that the “trigger” for the panel would be across-the-board spending cuts to entitlements and the Defense Department’s budget if the 12 lawmakers on the special committee fail to reach a deal.

Sources confirmed Sunday night that the last obstacle to settling the trigger issue is determining the level of the defense cuts. Republicans would like cuts limited to 2 percent of total DOD spending, while Democrats are pushing for 3 percent.

With Senators refusing to answer questions from a swarm of reporters following them across the Capitol, it is unclear how the enforcement mechanism was settled. But for Reid to hold votes soon indicates that a deal is close to cooked. He will need 60 votes to send the measure to the House, where Boehner will face an even more complicated vote calculus given the conservative members of his Conference.

Jessica Brady contributed to this report.