Rep. Kevin McCarthy speaking from an event at the southern border in El Paso, Texas, on November 22, 2022.
CNN  — 

Kevin McCarthy on Tuesday demanded the resignation of Homeland Security Secretary Alejandro Mayorkas and warned of potential impeachment proceedings if he doesn’t step down, marking the House Republican leader’s strongest comments on the matter to date as he scrambles to lock down the votes for his speakership.

McCarthy, speaking from an event at the southern border, said that when Republicans take over the House in January, they will “investigate every order, every action, and every failure” to determine if they should begin impeachment proceedings.

“Our country may never recover from Secretary Mayorkas’ dereliction of duty. This is why today I am calling on the secretary to resign,” he said. “If Secretary Mayorkas does not resign, House Republicans will investigate every order, every action and every failure. And we will determine whether we can begin an impeachment inquiry.”

The Department of Homeland Security said in a statement that Mayorkas has no plans to resign and called on Congress to come up with legislative solutions to fix the nation’s broken immigration system. The agency continues to maintain that the border is secure, but has acknowledged it is dealing with an unprecedented number of noncitizens seeking to enter the country and that shifting demographics have added to the migration challenges they are facing.

“Secretary Mayorkas is proud to advance the noble mission of this Department, support its extraordinary workforce, and serve the American people. He has no plans to resign,” a DHS spokeswoman said in a statement. “The Department will continue our work to enforce our laws and secure our border, while building a safe, orderly, and humane immigration system. Members of Congress should come to the table and work on solutions for our broken system and outdated laws, which have not been overhauled in over 40 years.”

While McCarthy and top Republicans have repeatedly promised to launch rigorous investigations into problems at the southern border, McCarthy had – up until this point – largely tamped down impeachment talk, saying they would not pre-determine the outcome or use impeachment as a political weapon and would follow the facts wherever they lead next year.

McCarthy’s shift in tone comes as he is facing a rebellion from his right flank in the speaker’s race, with at least five House Republicans vowing to vote against him on the floor in January. One of the complaints about McCarthy from the GOP hardliners is that he isn’t aggressive enough when it comes to investigations and impeachment.

The right flank has been agitating to impeach Mayorkas in particular, though others in the party are skeptical that the secretary’s actions meet the bar of high crimes and misdemeanors. Impeaching a Cabinet official has only happened once in US history.

McCarthy – who was nominated by his party last week to serve as speaker – made his comments about Mayorkas from El Paso, Texas, where he and a group of House Republicans met with border patrol agents and received an operational briefing earlier in the day.

“We spent the day with border agents,” McCarthy said at a news conference following their visit. “I asked each and every one that this border is secure. They laughed. They said it is not; it is one of the worst points in the history of this nation.”

When pressed on what potential crimes Republicans would investigate, McCarthy responded: “Lying to the American public, withholding ICE from doing their job, not following through on what the laws in the books are today.”

White House press secretary Karine Jean-Pierre responded to McCarthy’s planned visit to the US-Mexico border earlier Tuesday by asking what his plan is on immigration and accusing Republicans of having “no plan” and just “political stunts.”

“The question that we have for Kevin McCarthy – who is soon to be Speaker McCarthy – what is his plan? What is he doing to help the situation that we’re seeing. What is his plan? He goes down there and does a political stunt, like many Republicans do, that we have seen them do, but he actually is not putting forth a plan,” Jean-Pierre said when asked about the White House reaction to McCarthy’s visit.

Republicans have already started to lay the groundwork for investigations related to the border next year. Top GOP lawmakers have requested a wide swath of documents related to the Biden administration’s enforcement of immigration policies and have formally told the White House that they’d like to possibly hold hearings and conduct transcribed interviews with Mayorkas and a number of other officials.

CNN’s Allie Malloy contributed to this report.