Senate Majority Leader Harry Reid (D-Nev.) said he would be open to allowing a vote on a balanced budget amendment to the Constitution and other compromises if Republicans are willing to cut a deal taking a debt default off of the table through 2012.

“If people want a vote on that, fine,” Reid said of the balanced budget amendment Friday.

But the House plan’s short-term increase and requirement for the actual passage of an amendment to the Constitution — not just a vote — are poison pills in the Senate, Democrats said.

“It’s really time they legislate,” Reid said.

Reid’s No. 3 lieutenant, Conference Vice Chairman Charles Schumer (N.Y.), said the GOP bill would “guarantee” a default because the amendment would never pass the Senate, and Majority Whip Dick Durbin ripped the GOP plan for turning the Constitution into a “bargaining chip.”

“I wish Robert Byrd were still here,” he said, referencing the late West Virginia Democrat who was known as the “dean of the Senate” and a self-taught constitutional scholar.

Reid, meanwhile, repeated his call on Senate Minority Leader Mitch McConnell (R-Ky.) to meet with him and help find a solution later today.

“I’m confident he will,” Reid said.

Democrats said they are heading toward a 1 a.m. vote Sunday on their own plan if a bipartisan deal isn’t reached later today.

Reid said he was open to adding McConnell’s fallback language to Reid’s own deficit reduction plan. McConnell’s Plan B proposal would allow President Barack Obama to raise the debt limit in three stages over the next 17 months, but Congress could block that by passing a resolution of disapproval and possibly overcoming any presidential veto.

Senior Democratic leadership aides said the Reid bill now includes additional savings from mandatory programs. Aides said the plan now would cut $2.5 trillion from the deficit over 10 years. Democrats initially said the package would cut $2.7 trillion from the deficit, but the Congressional Budget Office scored it as $2.2 trillion.

Reid also showed a willingness to consider triggers that would force Congressional action on a deficit reduction plan. Both Reid’s proposal and Boehner’s plan would create such a committee, but Reid said he would be open to allowing other Senators, such as the bipartisan “gang of six,” to force their proposals to the floor if that panel deadlocks.

But Reid said Republicans haven’t yet been willing to come to the table.

“I’m happy to look at different alternatives,” he said.

Other Democrats also suggested including trigger mechanisms Friday, including Obama, Senate Budget Chairman Kent Conrad (N.D.) and Durbin.

Durbin and Conrad — both members of the gang of six — said any trigger would have to inflict pain for both parties if the joint committee fails to devise a deficit reduction package. That means a trigger could not just target more spending cuts, and Obama said any enforcement mechanism would have to be “smart and balanced.”

Conrad said a trigger is being developed that would include spending cuts and tax increases.

“We spent a lot of time on it, but we will just have to see,” Conrad said. “We have not had a chance to share it broadly on their side.”

Humberto Sanchez contributed to this report.