Debt limit deal on track to clear key hurdle ahead of final House vote

House Speaker Kevin McCarthy helped secure a debt limit deal - now he has to secure its passage in the House, with little room for error and a looming threat to his speakership.

In a win for McCarthy, a key Republican said he expects to support a rule to set parameters for debate. The powerful House Rules Committee must still vote to adopt the rule, but with that anticipated support, it is now on track to do so - a hurdle that must be cleared before the bill can come to the House floor for a final vote.

"I want to see the rule (first) it's not printed yet, it's not been read, but I anticipate voting for this rule," GOP Rep. Thomas Massie of Kentucky said as the committee met to consider the debt limit bill. It had previously been unclear how Massie planned to vote. If he did not support the rule, the debt limit bill may have been unable to advance to the House floor.

The timeframe to get the bill passed through both chambers of Congress and signed into law is extremely tight. Lawmakers are racing the clock to avert a catastrophic default ahead of June 5, the day the Treasury Department has said it will no longer be able to pay all of the nation's obligations in full and on time.

In another positive sign for the bill's prospects in the House, a wide range of members on both sides of the aisle - many of them moderates - appear poised to coalesce behind the deal to avert default. Republicans believe they are pushing toward 150 Republican votes or more, two sources told CNN.

That's more than a majority of the Republican conference, which McCarthy has been promising for days he could get on the bill.

To win the speakership, McCarthy agreed to name three conservative hardliners - GOP Rep. Chip Roy of Texas, Massie and Rep. Ralph Norman of South Carolina - to the Rules committee, a major concession since usually the panel is stacked with close allies of the leadership.

Roy and Norman have both emerged as leading critics of the bipartisan debt limit bill.

In January, Massie told CNN he was reluctant to vote against rules to stop bills in their tracks.

"I would be reluctant to try to use the Rules Committee to achieve a legislative outcome, particularly if it doesn't represent a large majority of our caucus," Massie said at the time. "So I don't ever intend to use my position on there to like, hold somebody hostage - or hold legislation hostage."

Another key concession McCarthy made to win the speakership that looms over the effort to push the debt limit deal: Any member of the House can move to force a vote to topple the speaker known as a motion to vacate.

Roy made the strongest threat yet to McCarthy's gavel during an interview with Glenn Beck, saying that if the deal can't be killed in rules or on the floor: "Then we're going to have to then regroup and figure out the whole leadership arrangement again."

The comments were confirmed to CNN though his spokesperson.

Republican Rep. Jim Jordan of Ohio said Tuesday that he's not worried about McCarthy's speakership. "I think he is doing a good job," he said.

Rep. Patrick McHenry said Tuesday he was not worried about McCarthy losing his speakership and defended the deal he helped cut.

"With a narrow majority in the House, we have the most conservative outcome we possibly could," McHenry said.

"I'm proud of the package. I wanted more. I absolutely wanted more, (but) what we have here is better than what was about to come."

Asked if the speaker's job is now in jeopardy, McHenry said, "no."

This story and headline have been updated with additional developments.

CNN's Manu Raju and Morgan Rimmer contributed to this report.