“We've got serious business here. We have important work to do,” she added.

The back-and-forth comes after a series of clashes last week following Pelosi's veto of two of McCarthy’s GOP picks to serve on the Jan. 6 investigation: Reps. Jim Banks of Indiana and Jim Jordan of Ohio, both of them avid Trump defenders. The move prompted McCarthy to withdraw all of his appointees to the select committee in protest, describing the investigation as a partisan effort designed to hurt Trump and the party ahead of next year’s midterms. Republicans, however, largely opposed a bipartisan Jan. 6 commission earlier this year.

House Republicans forced a vote Monday evening in an effort to seat all of McCarthy’s picks for the committee, but the Democratic-controlled House voted down the measure. Cheney and Kinzinger joined every Democrat in voting to table the proposal.

Cheney was part of Pelosi’s initial wave of names tapped to serve on the panel that will examine the deadly events of Jan. 6, when Trump supporters breached the Capitol in an attempt to disrupt certification of the ex-president's election loss, forcing lawmakers and then-Vice President Mike Pence to flee.

Following the GOP boycott, Pelosi on Sunday named Kinzinger to the Jan. 6 committee, giving Democrats two House Republican members who they say boost their panel’s bipartisan credibility.

Kinzinger, wearing a tie patterned with elephants, also called McCarthy’s comments “childish" during a break in the select panel prep session.

“He can call me whatever names he wants,” Kinzinger said, adding that the bottom line is “I’m a Republican.”

Still, McCarthy’s jab signals a remarkable shift from earlier this year. Cheney once served as his leadership partner before her frequent Trump criticisms prompted her colleagues and fellow leaders to eject the Wyoming Republican from a role that is responsible for the conference’s messaging.

These days, some of Cheney and Kinzinger's fellow Republicans are openly speculating about their future in the House GOP conference. Asked whether the duo should face sanctions from their party for accepting Pelosi's appointment to the inquiry, McCarthy said only that "we'll see."

But Kinzinger shrugged off the subtle threat on Monday: “If the conference decides” to punish him and Cheney, he said, it “says more about them than it does about us."

Kinzinger also didn’t rule out calling his fellow Republican members to testify before the select panel, saying it was “important” to hear from them if they had relevant information. Discussions are still ongoing about the scope of Republican staff for the inquiry, he added, but he lauded former Rep. Denver Riggleman (R-Va.) as a model for those hires.

No matter how actively McCarthy tries to tether Cheney and Kinzinger to Pelosi, who frequently appears in GOP attack ads, they both have strong conservative voting records to counter his attacks. House Majority Leader Steny Hoyer noted as much, while arguing Monday that Cheney and Kinzinger are “real Republicans.”

“If anybody looks at the voting records of Mr. Kinzinger and Ms. Cheney, they will know that they haven’t voted with Speaker Pelosi except on the most bipartisan of bills,” Hoyer said. “These are people who come from conservative Republican districts who have represented Republican values. The difference is, and this is the key, they both believe in the truth. That ought not to be a partisan issue.”

Nick Niedzwiadek contributed to this report.