Updated: 12:25 p.m.

Speaker John Boehner acknowledged he and his leadership team have begun working on a plan to address the debt limit if, as expected, the conservatives’ Cut, Cap and Balance plan does not make it out of the Senate.

“I’m not going to give up hope on Cut, Cap and Balance. But I do think its responsible to look at what [a] Plan B would look like. The leadership had a long conversation yesterday about Plan B. There are a lot of options available to us,” the Ohio Republican told reporters Tuesday.

Boehner, who has continued to meet with President Barack Obama since talks collapsed last week, also doubled down on the GOP’s assertion that by even agreeing to discuss the need for a debt limit increase, Republicans have already compromised.

In fact, Boehner sought to cast the Cut, Cap and Balance plan as a “balanced” bill, arguing that Obama “gets his increase in the debt limit” and in exchange, Republicans would get massive cuts in discretionary spending, caps on future spending and a balanced budget amendment.

While Boehner has more than enough Republican votes to pass the bill in the House, it has virtually no chance of passage in the Senate — and Obama has already said he would veto the Cut, Cap and Balance Act.

Although Boehner did not provide details on what possible alternatives he is considering, the acknowledgement comes as he is under increasing pressure from conservatives to publicly abandon a separate Plan B proposal by Senate Minority Leader Mitch McConnell (Ky.) and insist on the Cut, Cap and Balance plan.

Freshman Rep. Joe Walsh is calling on House GOP leaders to denounce McConnell’s plan to raise the debt ceiling ahead of the Aug. 2 deadline.

“We strongly urge you to both publicly oppose Senator McConnell’s plan to raise the debt ceiling and ensure it never comes to the House floor for a vote,” the Illinois Republican wrote in a letter to be sent to Boehner and House Majority Leader Eric Cantor (R-Va.) later this week. The letter has more than 20 co-signers and the backing of the Club for Growth.

House Republicans have largely dismissed McConnell’s plan, charging it would give Obama too much authority by allowing him to raise the debt ceiling by $2.5 trillion without any guarantee that spending cuts would also be made. The proposal would require Obama to request debt limit increases along with suggested offsets. Congress would be permitted to vote on resolutions of disapproval, but the president could veto those resolutions, under the plan. A supermajority is needed to overturn a presidential veto.

McConnell and Senate Majority Leader Harry Reid (D-Nev.) are in talks to find a solution that would marry the Kentucky Republican’s proposal with a joint committee charged with crafting a broader deficit reduction package. But Walsh and other House Republicans remain staunchly against shifting the responsibility of raising the debt limit away from Congress and to Obama.

“McConnell’s plan supersedes the rights of the American people,” Walsh’s letter states. “The only way for average American families to act on the debt ceiling is through their elected representatives in Congress.”

The letter also declares, “Senator McConnell’s plan is business as usual and does not offer any real solution to runaway spending.”

Walsh is one of 87 new GOP lawmakers who is digging in his heels on raising the debt limit, which is projected to exceed its current ceiling by Aug. 2. Conservative grass-roots group Heritage Action has said it will make any vote on the McConnell plan a “key vote” and are urging Membtodayers to sign Walsh’s letter. Another group of mostly freshman lawmakers is expected to travel down Pennsylvania Avenue to the White House on Tuesday to call on Obama to put forth his own deficit reduction plan.