House Republican leaders began preparing their members on Tuesday to accept a potential deficit deal that includes new tax revenues.

The GOP co-chairman of the deficit supercommittee, Rep. Jeb Hensarling (R-Texas), briefed the House Republican Conference on the details of multiple offers that GOP members of the panel have made to their Democratic counterparts.

{mosads}A week before the supercommittee’s Nov. 23 deadline, a deal has yet to be struck, but Tuesday’s meeting offered Hensarling his first chance to explain to his restive colleagues what Republicans have described as a major concession in negotiations with Democrats. 

Lawmakers emerged from the closed-door meeting saying Hensarling had made the case that offering some new revenue — $300 billion in at least one publicized offer — would be a good trade to secure a permanent extension of the George W. Bush-era tax rates.

Speaker John Boehner (R-Ohio) told reporters after the briefing that the GOP had made “a fair offer,” referring to a proposal from supercommittee member Sen. Pat Toomey (R-Pa.) that would call for about $300 billion in new taxes in a total deficit-reduction package of $1.2 trillion.

“Both Democrats and Republicans have all done good work, they’ve worked very hard, but there isn’t an agreement,” Boehner said. “I’m convinced that if there is an agreement that it can, in fact, pass.”

Despite the concession on taxes, Democrats have rejected the GOP offer as “not serious.” 

Hensarling received a standing ovation following his presentation, which one Republican described as “clinical” and somewhat “detached.”

Amid widespread skepticism that the committee will meet its $1.2 trillion charge, some members said Hensarling had dampened expectations for a blockbuster deal.

One lawmaker who attended the conference told The Hill that Hensarling “did say that what with the statutory obligations that have been set before us, let alone the statutory goals — don’t be surprised if they’re not met.”

Freshman Rep. Bobby Schilling (R-Ill.) said he came away thinking that any agreement would not greatly exceed $1.2 trillion.

“It doesn’t sound like it’s going to be anything major,” Schilling said.

Dozens of lawmakers and outside groups are still pushing for the debt panel to “go big” and cut at least $4 trillion from the deficit. A group that organized a letter signed by more than 100 House Democrats and Republicans will hold a second press conference on Wednesday calling for a grand bargain.

Meetings involving members of the supercommittee continued throughout the day. Boehner met privately with Senate Majority Leader Harry Reid (D-Nev.) on Tuesday morning, in an indication that congressional leaders are taking a more active role in the deficit talks. Boehner and Senate GOP Leader Mitch McConnell (Ky.) met later in the day with Republican members of the panel.

The question of revenues proved once again to be at the center of the debate within the conference. Some conservatives have said they are concerned with the GOP’s offer, especially considering the pledge most of them signed to oppose any net tax increase 

According to Schilling, Hensarling made no direct reference to Grover Norquist, the author of the anti-tax pledge, but he brought up pledges in general, and said that “his pledge is to the people of his district.”

Hensarling focused on the benefit of preventing a much larger tax increase if the Bush tax rates were allowed to expire in 2013. One lawmaker called Hensarling’s presentation to his colleagues a bit of “covering their rear because obviously the anti-tax guys were all upset so he was walking through how when the Bush tax cuts expire, they’re going up more than that anyway, so it’s not a tax increase.”

Hensarling acknowledged that time was running short as he left a meeting in Boehner’s office shortly before 6 p.m.

“It’s getting late, but again, haven’t given up hope. But it is getting late,” he told reporters.

GOP Reps. Jeff Flake (Ariz.), Mike Pompeo (Kan.) and Tim Scott (S.C.) said they hadn’t decided whether they could support the GOP offer.

House Budget Committee Chairman Paul Ryan (R-Wis.) stood by the GOP offer.

{mossecondads}“It think it was a strong attempt to try to break a logjam,” he said.

He noted that the offer included extension of the Bush-era tax rates set to expire in 2013.

“Held up against a big tax increase that is coming, I’ll take that any day,” he said.

Hensarling, lawmakers said, cast the Democratic members of the debt panel as divided, hindering progress toward a deal.

“The Republicans’ problem has been that they are not dealing with a Democrat Party that’s been cohesive in their position,” Rep. Scott Garrett (R-N.J.) said after the meeting.

He said Hensarling told them Republicans had put forward multiple offers and were “waiting to see if the Democrats could speak with one voice.”

A Democratic member of the panel, Rep. James Clyburn (S.C.), acknowledged on Sunday that Democrats had “not coalesced” around a $2.2 trillion offer.

“Well, you know, that is a Democrat’s plan. It’s not the Democratic plan. There are six Democrats on this committee, and though I have a great deal of admiration and respect for all of them, the fact of the matter is, Democrats have not coalesced around a plan,” Clyburn said on “Fox News Sunday.”

— Molly K. Hooper and Alexander Bolton contributed to this article.