House Republicans, who are just weeks away from taking control of the House of Representatives, are already indicating that border security and illegal immigration will be among the issues top of their agenda when they take the gavel early next year.

Republican gains in the recent midterm elections have handed the GOP control of the House, although the Senate will remain in Democratic hands. Within days of House control being confirmed, Republicans have already made it clear that the ongoing crisis at the border will be a priority.

That was highlighted this week when GOP Leader Kevin McCarthy led a delegation to the southern border -- and called on Homeland Security Secretary Alejandro Mayorkas to either resign or face a potential impeachment inquiry next year.

"He cannot and must not remain in that position," McCarthy said. "If Secretary Mayorkas does not resign, House Republicans will investigate every order, every action and every failure to determine whether we can begin an impeachment inquiry."

DHS PUSHES BACK AGAINST MCCARTHY CALL FOR MAYORKAS TO RESIGN OR FACE POTENTIAL IMPEACHMENT 

McCarthy said he had spoken to Reps. Jim Jordan and James Comer, the ranking Republicans of the Judiciary and Oversight Committees, respectively, and said they have his complete support to investigate the "collapse" of the border.

"The American public deserves more, deserves better and expects more within their government. Enough is enough. We will do whatever it takes," he said.

The U.S. has been hit by a nearly two-year long border crisis that saw more than 1.7 million migrant encounters in FY 2021 and over 2.3 million in FY 2022. October has indicated that that surge is likely to continue, as more than 230,000 hit the border in that month alone.

Separately, a federal judge recently ordered the government to wind down the use of the Title 42 public health order, which has been used to expel a majority of migrants at the border since March 2020. That has led to fears of an even bigger surge and more chaos as more migrants are released into the U.S.

Republicans have long been hammering the Biden administration over its handling of the crisis, arguing that officials have fueled the crisis by rolling back Trump-era policies and narrowing interior enforcement. The Biden administration has said that the crisis is hemisphere wide, and has called on Congress to act to fix broken U.S. immigration laws.

"Members of Congress can do better than point the finger at someone else; they 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," a DHS spokesperson said on Wednesday.

MCCARTHY CALLS ON MAYORKAS TO RESIGN OR POTENTIALLY FACE IMPEACHMENT INQUIRY: ‘ENOUGH IS ENOUGH’

Republicans in July unveiled a number of policy proposals to secure the border that they said they would advance if they took the House. Policies include finished the Trump-era border wall, expanding Title 42, modernizing technology and overhauling the asylum system.

"I think we're going to be very aggressive, and I think the administration will have some choices to make," House Homeland Security Committee Ranking Member John Katko told Fox in July. "Do they want to spin their wheels for two years and get nothing done or do they want to work with Republicans if the Republicans are in the majority and start doing some of the things that Republicans want?"

HOUSE GOP PUTS MAYORKAS, DHS ON NOTICE: GIVE ‘UNFETTERED COOPERATION' OR BE COMPELLED TO TESTIFY

In addition to his suggestion that multiple House committees will be firing on all cylinders in investigating the crisis, McCarthy also said that he intends to have hearings physically at the border, so that Democrats can witness the crisis firsthand.

Separately, Judiciary Committee Ranking Member Jim Jordan drew battle lines with the administration this week, sending a letter with other lawmakers calling for "unfettered cooperation" from Mayorkas and other DHS officials in testifying to the committee next year.

The Republicans asked DHS to prepare these officials to appear in-person for committee hearings or provide transcribed interviews, threatening to "resort to compulsory process" if the department and its sub-agencies do not comply. 

Also this week, Jordan, along with Senate Judiciary Ranking Member Chuck Grassley, sent a request for documents and information about a Venezuelan parole program that they believe is in violation of federal law.

McCarthy, meanwhile, is likely to face continued pressure from the right of his caucus on the matter if he does not keep up the pressure on the administration on the border security issue. Rep. Andy Biggs, who is co-chair of the border security caucus, expressed his dissatisfaction with McCarthy’s announcement. 

"Mayorkas needs impeached. Period. No hesitation," he said.

Fox News' Chris Pandolfo and Bill Melugin contributed to this report.