Senate Democrats on Tuesday were not able to reach an agreement on proposed changes to the chamber’s rules, but Majority Leader Harry Reid indicated the end of the long debate was near.

Following a meeting of the Democratic Conference that lasted more than two hours, the Nevada Democrat predicted that his party would reach a deal by the end of the week. Still, it appears that any substantive changes to filibuster rules are unlikely.

“We are working our way through that,” Reid told reporters. “I think we have a way to proceed forward. I hope we move this down the road in the next 24 to 48 hours.”

The Senate has been frozen since the start of the 112th Congress as Reid and other Senate leaders have tried for the past three weeks to negotiate the issue with a group of mostly junior Democrats. The less-senior lawmakers want to change the Senate filibuster rules and other procedures that have been used by the minority to slow debate.

Reid bought more time for the negotiations by using a procedural maneuver on Jan. 5 that allowed him to hold open the first legislative day of the session.

During their separate caucus lunches Tuesday afternoon, Senators from both parties listened to pitches from their respective leaders about a deal that would restrict the use of secret holds and allow some nominees and Cabinet officials to advance unchallenged by the minority party.

Also under the agreement, hatched by Republican Conference Chairman Lamar Alexander (Tenn.) and Democratic Policy and Communications Center Chairman Charles Schumer (N.Y.), Democrats would no longer use procedural tactics to block GOP amendments to bills on the floor.

Asked how the presentation was received inside the Republican meeting Tuesday afternoon, Alexander told reporters: “Well, they didn’t throw me out of the room. I’m still the Conference Chairman.”

Alexander said Republicans ultimately just wanted the Senate to function better and were amenable to making the body more functional, but said no agreement on the terms of the deal had been made.

“What we really want, and I think what most Democrats want, we’d like for most bills to come to the floor, and for most Senators to be able to offer amendments and debate,” he said. “Several of our Members and several Democratic Members still have decisions to make, and when we finish, Sen. Reid and [Minority Leader Mitch] McConnell will go to the floor and announce an agreement, when there is an agreement.”

Schumer did not comment on the discussions as he left the Democratic meeting. But several Democrats indicated discussions were ongoing on a number of proposed changes.

Sen. Claire McCaskill, who has advocated for removal of secret holds on bills, was optimistic as she departed the Democratic caucus.

“I really am very, very hopeful that we will get way more than 67 votes to do away with the secret hold,” the Missouri Democrat said. “I think it may be the shining star of bipartisan accomplishment in terms of making the Senate more transparent and accountable to the people.”

Sen. Amy Klobuchar, a supporter of changing the filibuster rules, said a vote on changes to those rules was still a possibility.

“We are having very good discussions and have been making progress,” the Minnesota Democrat said. “Stay tuned.”

To further emphasize that the debate over changes to the rules was not over, Sens. Jeff Merkley (D-Ore.), Tom Udall (D-N.M.) and Tom Harkin (D-Iowa) took to the Senate floor to advocate for a vote to change the filibuster rules.

David M. Drucker and Steven T. Dennis contributed to this report.