But one of Roy's colleagues disputed his recollection of events in a statement to CNN producer Morgan Rimmer.

According to Rimmer, Rep. Dusty Johnson (R-SD) told her that "if those conversations took place, the rest of the conference was unaware of them. And frankly, I doubt them. I haven't talked to the speaker about them yet today, but I would be a little surprised if that was a kind of a commitment."

CBS News reported on Monday that "the House Rules Committee will hold a hearing at 3 p.m. Tuesday, which will determine the rules and length of time for debating the bill and any amendments that would be allowed."

According to Reuters, "The agreement would suspend the debt limit through Jan. 1 of 2025, cap spending in the 2024 and 2025 budgets, claw back unused COVID funds, speed up the permitting process for some energy projects, and include extra work requirements for food aid programs for poor Americans. The 99-page bill would authorize more than $886 billion for security spending in fiscal year 2024 and over $703 billion in non-security spending for the same year, not including some adjustments. It would also authorize a 1% increase for security spending in fiscal year 2025."

Although CBS noted that the measure is likely to pass with bipartisan support, dissent within the GOP may hamper McCarthy's pledge to send the legislation to the Senate this week.

Any unforeseen snags increase the risks of the Treasury Department running out of money, which Secretary Janet Yellen has repeatedly warned could occur in early June.

"Once the bill reaches the Senate, where Democrats have the majority, the pace of action will largely depend on whether any senators try to hold up the bill, possibly with amendment votes. That could tie up the legislation for a few days," CBS explained.