As the government was reopening Thursday morning, the four leaders of the new budget conference committee broke bread in an ornate room named for a legendary dealmaker.

“We had a very good conversation. We decided to discuss how we’re going to proceed over breakfast. We want to look for ways to find common ground, to get a budget agreement,” House Budget Chairman Paul D. Ryan, R-Wis., told a gaggle of reporters and camera gathered outside the Lyndon B. Johnson room.

Ryan’s Senate counterpart, Patty Murray, conceded the challenges ahead in trying to reconcile the Democratic and Republican budget blueprints by a Dec. 13 deadline agreed to as part of the Senate deal to suspend the debt limit and end the government shutdown.

“Chairman Ryan knows I’m not going to vote for his budget. I know that he’s not going to vote for mine,” the Washington Democrat said. “We’re going to find the common ground between our two budgets that we both can vote on, and that’s our goal.”

The two plans aren’t at all similar, with the Senate calling for finding significant revenue increases and the House seeking major savings from an overhaul of entitlements.

“We have agreed we are going to look at … everything in front of us and we know that it’s going to be a challenge, but we believe we can find common ground,” Murray said.

“Not talking guarantees failure,” House Budget Committee ranking member Chris Van Hollen of Maryland said. “Talking doesn’t guarantee success, but if you don’t get together, obviously you can’t move forward.”

The four leaders of the conference committee, which includes Alabama GOP Sen. Jeff Sessions, seemed acutely aware of the scale of the challenge, as do the rank-and-file members involved — a point emphasized early Thursday morning by Senate conferee Angus King on CNN.

“I was sitting on the floor of the U.S. Senate when Patty Murray said who the conferees were going to be. My first thought, ‘Wow, that’s pretty cool.’ My second thought was, ‘Holy smokes, we have to get this done,'” said King, a Maine independent who caucuses with the Democrats.

Speaking with reporters after the formal availability, Van Hollen said it would be up to Murray and Ryan to set the schedule, but that it would not be like the spectacle of the ill-fated deficit reduction panel that helped lead to the sequester. Van Hollen declined to speculate on how many meetings would be held publicly with C-SPAN cameras in the room.

“It’s like any conference committee,” Van Hollen said. “It is important to focus on that. This is not a repeat of the supercommittee. This is a conference committee on the budget, and so we’ll proceed like any conference committee.”