House Speaker Kevin McCarthy is safe in his position after reaching a debt-ceiling deal with President Biden that almost a third of his Republican caucus voted against, a key GOP negotiator said.

House Speaker Kevin McCarthy of Calif. along with other Republican members of the House, speaks at a news conference after the House passed the debt ceiling bill at the Capitol in Washington on Wednesday, May 31. The bill now goes to the Senate. Jose Luis Magana/Associated Press

Representative Garret Graves, who was part of McCarthy’s negotiating team with the White House, was asked about comments last week by fellow Republican Ken Buck that the speaker should be concerned about his political future.

“It is not a mainstream position,” Graves said on CBS’s Face the Nation on Sunday. “I’ll tell you right now: Speaker McCarthy’s position is absolutely safe.”

With Republicans holding a nine-seat edge in the House, speculation about McCarthy’s vulnerability to ultraconservative House members intensified as the debt-ceiling accord emerged.

Seventy-one House Republicans ended up voting against the measure, arguing it fell short of their demands for spending cuts, while 149 supported it, allowing McCarthy to avoid an imminent vote to vacate the speaker’s chair.

“I don’t know if a motion to vacate is going to happen right away,” Buck said Sunday on CNN’s State of the Union. “I do know that Speaker McCarthy has credibility issues.”

However, a motion to end McCarthy’s speakership couldn’t be done “by just a few people,” Buck said. “I think there has to be a consensus in the conference, the Republican Conference.”

Biden on Saturday signed the legislation, which averts a first-ever U.S. default, limits federal spending for two years, and suspends the debt ceiling through the 2024 election.

Asked on May 28 whether he was worried about a possible effort by hard-line conservative lawmakers to oust him from the speaker’s chair, McCarthy said: “Not at all.”