Facing a right-wing revolt against his campaign to become the next House speaker, Representative Kevin McCarthy, Republican of California, on Tuesday visited the southwest border and called on Alejandro N. Mayorkas, the Homeland Security secretary, to resign or face potential impeachment proceedings.
At a news conference in El Paso, Mr. McCarthy, who has suffered defections in recent days from hard-right Republicans who have said they would not back him for speaker, accused Mr. Mayorkas of ignoring immigration laws and lying to Congress, citing the secretary’s assertions that the border is secure at a time when crossings are at a high.
“If Secretary Mayorkas does not resign, House Republicans will investigate every order, every action and every failure, and will determine whether we can begin an impeachment inquiry,” Mr. McCarthy said in front of a bank of television cameras.
The threat was not a new one — Mr. McCarthy made a similar trip last spring and warned then that a G.O.P. Congress would consider impeaching Mr. Mayorkas — but it was a striking change in tone from a leader who had spent the weeks before the midterm elections playing down the possibility that Republicans would use their power to impeach President Biden or members of his administration.
While Mr. McCarthy did not commit on Tuesday to following through on the threat to Mr. Mayorkas, he strongly hinted he was inclined to do so.
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“We never do impeachment for political purposes,” Mr. McCarthy said when asked what specific crimes the secretary may have committed. He added: “We know exactly what Secretary Mayorkas has done.”
It reflected the pressure Mr. McCarthy is under from the extreme right of his party to use the House majority to aggressively attack the Biden administration. The dynamic has intensified in recent days, as right-wing Republicans have refused to support Mr. McCarthy for speaker, imperiling his chances of drawing the 218 votes he needs on the House floor to secure the top post.
After a poorer than expected performance in the midterm elections, Republicans control just 219 House seats, with a handful of races still uncalled. They are on track to gain only a few more, giving Mr. McCarthy very little room for defections and leaving him looking for ways to placate members on his right flank.
Representative Andy Biggs, Republican of Arizona and a former chairman of the hard-right Freedom Caucus, has said that Mr. McCarthy does not have the votes needed to become speaker in a floor vote on Jan. 3. Mr. Biggs challenged Mr. McCarthy last week for the party’s nomination for the speakership. Mr. McCarthy prevailed, but the tally pointed to an uphill battle; he lost three dozen Republican votes.
Several others have since publicly indicated they would not back Mr. McCarthy, including Representatives Matt Gaetz of Florida, Bob Good of Virginia, Matt Rosendale of Montana and Ralph Norman of South Carolina, who told Politico on Tuesday that he was a “hard” no and expected “many more” Republicans to take the same position.
Immigration advocacy groups condemned Mr. McCarthy’s news conference on Tuesday as a political stunt.
“Instead of a serious reckoning with their party’s underwhelming midterm results and real efforts to distance themselves from MAGA extremism and the violence it inspires, McCarthy’s trip is a sign they plan to double down and again push ugly and dangerous rhetoric about immigrants and the border,” said Vanessa Cárdenas, the director of America’s Voice.
Before the elections, Mr. McCarthy said he had yet to see grounds for impeaching any Biden administration official, but hard-right members of his rank and file have been pressing to target the president and several members of his team including Vice President Kamala Harris, Secretary of State Antony J. Blinken, Attorney General Merrick Garland and Mr. Mayorkas.
Overall, 10 House Republicans have either introduced or sponsored a total of 21 articles of impeachment against Mr. Biden and his top officials since the start of the administration.
In a recent interview with The New York Times Magazine, Representative Marjorie Taylor Greene, Republican of Georgia, shrugged off Mr. McCarthy’s equivocation about impeachment.
“I think people underestimate him, in thinking he wouldn’t do it,” she said, adding that a Speaker McCarthy would give her “a lot of power and a lot of leeway” in order to fulfill his job and “please the base.”
Shortly afterward, Ms. Greene announced she would back Mr. McCarthy’s bid for speaker.