Other Republicans, however, were already coming out against the bill.
In a statement, Republican Study Committee Chairman Jim Jordan (Ohio) rejected the plan outright.
"While I thank the Speaker for fighting for Republican principles, I cannot support the plan that was presented to House Republicans this afternoon," Jordan said.
"The Senate should resume debate on the Cut, Cap, and Balance Act, amend it if necessary, and pass it, so we can provide the American people a real solution," he added.
Rep. Tim Huelskamp (R-Kan.), a freshman conservative, also issued a statement in which he said he would not support the bill.
It is unclear how deep distrust of Boehner's plan goes. Only nine Republicans voted against the Cut, Cap and Balance bill last week, and only 39 Members have signed a pledge that commits them to supporting a debt limit increase only if a balanced budget amendment has first been passed. The chances of such a constitutional amendment clearing both chambers this year are dim.
Cole downplayed opposition to Boehner's plan, asserting, "This is a potentially career-defining vote ... so in those situations you always have to talk Members through" them.
Cole also said that unlike during the fight earlier this year over government funding and a continuing resolution, Boehner has "a united leadership behind him. It's very important that he has [Majority Leader] Eric Cantor [R-Va.] behind him; it's very important that he has [Majority Whip] Kevin McCarthy [R-Calif.] behind him."
Still, that sort of trust is not necessarily a given for Boehner. Unlike Minority Leader Nancy Pelosi (Calif.), who had a tight grip on her majority during her run as Speaker, Boehner has opted for a more open approach to leadership.
While some had thought a looser form of leadership would help the Conference mature quickly, it has instead given running room to conservatives who have proved to be a problem for Boehner's leadership style throughout the debt ceiling talks. In fact, outside organizations were already ramping up their opposition to Boehner's plan Monday afternoon.
In a statement, the Cut, Cap and Balance Coalition, which was instrumental in pushing the GOP to back its plan in the first place, rejected Boehner's proposal.
"To be clear, we are not criticizing the Speaker; however, we cannot support his framework, and we urge those who have signed the Pledge to oppose it and hold out for a better plan," the group said.
While Boehner attempts to sell his plan to stubborn conservatives, Senate Democrats introduced an administration-backed plan with $2.7 trillion in savings, with no revenues and no entitlement reform. Senate Majority Leader Harry Reid (D-Nev.) said Monday that he would start the time-consuming procedural processes to have a vote on the package this week.
But time constraints threatened Senate action, especially considering the Reid bill has already been declared a nonstarter in the House.
Because any one Senator can hold up legislation, staging a filibuster is "one possibility" and "something that's come up in conversation and is being considered," said a GOP aide to a conservative Senator. The aide added a caveat: "Considering things are so liquid now, until there's more hard information, I don't think it's fair to speak to whatever the tactics will be." A spokesman for Senate Minority Leader Mitch McConnell (R-Ky.) would not say whether the leader was explicitly discouraging Members from filibustering.
Rep. Bill Cassidy has his blood drawn by Alesha Barbour during a free hepatitis screening in the Rayburn House Office Building hosted by the Congressional Viral Hepatitis Caucus to recognize "National Viral Hepatitis Testing Day."
Roll Call has launched a new feature, Hill Navigator, to advise congressional staffers and would-be staffers on how to manage workplace issues on Capitol Hill. Please send us your questions anything from office etiquette, to handling awkward moments, to what happens when the work life gets too personal. Submissions will be treated anonymously.