Tensions are rising in the GOP House over how to tackle a topic many back enthusiastically: impeaching Department of Homeland Security (DHS) Secretary Alejandro Mayorkas.

Republicans are largely unified in opposition to the secretary, but while some want to go full bore right away, others see fast-track impeachment as a mistake, warning that it's important to build their case before the public.

“We made the argument that impeachment was rushed — the second impeachment — and I think that's not who we are as a party,” said Rep. Michael McCaul (R-Texas), a former prosecutor, in reference to the second impeachment of former President Trump.

McCaul said it's the committees of jurisdiction that should be leading the inquiry.

“We need to have hearings on this and we need to gather evidence and facts and, look, do I think the guy has done a terrible job? Yes,“ McCaul said. “Do I think he's been derelict in his responsibilities? Yes. But we need to get all this together, and do it in a methodical way.”

In some corners, Republicans are lining up at the chance to impeach Mayorkas.

After Rep. Pat Fallon (R-Texas) filed articles of impeachment against the secretary this week, Rep. Andy Biggs (R-Ariz.) quickly pledged his own resolution while suggesting he was the one who had actually taken the impeachment action first.

“I was the first Member of Congress to introduce impeachment articles against DHS Secretary Alejandro Mayorkas in 2021,” Biggs wrote on Twitter. “I will reintroduce these articles with even more justification very soon.”

Balancing the different interests will be another challenge for Speaker Kevin McCarthy (R-Calif.), who has signaled he supports a deliberate approach.

“House Republicans will investigate every order, every action. And every failure will determine whether we can begin impeachment inquiry,” he said in November, during a trip to the border.

Twenty lawmakers have signed on to Fallon’s resolution. While he said he doesn't want to preclude any investigation, Fallon wants to prompt his colleagues to start them immediately. 

“I think it's of vital import to get the ball rolling immediately. Because this is an emergency. This is break glass. This is something that we can't just sit around any longer and say, ‘Well, we'll do it in a month, we'll take it up in four months.’ Let's take it up right now,” he told The Hill.

Building a case for Mayorkas’s impeachment may not be as easy as some of his critics think.

For example, Fallon argues that Mayorkas lied to Congress in two different appearances, when saying both that the Biden administration has maintained operational control of the border and that the border is secure. 

Both points are largely a matter of opinion; impeachment statutes are typically reserved for “high crimes and misdemeanors.”

“Impeachment is a very serious topic, and it's one where the facts need to lead you to the results, not have a predetermined decision,” said Rep. Tony Gonzales (R), who represents the Texas district with the longest shared border with Mexico.

Homeland Security officials, so far, have not assigned staff to deal with potential impeachment inquiries.

“Secretary Mayorkas is proud to advance the noble mission of this Department, support its extraordinary workforce, and serve the American people.  The Department will continue our work to enforce our laws and secure our border, while building a safe, orderly, and humane immigration system," said Marsha Espinosa, a spokesperson for DHS.

“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 they have not updated in over 40 years,” she added.

Ultimately, Republicans who support impeachment and those who oppose it will have to make their case to McCarthy and his leadership team, who will weigh the costs and benefits of spending political capital on a historic measure with scant chances in the Senate.

Impeaching Mayorkas in the House would require a majority vote. In the Senate, a two-thirds majority would be necessary to win a conviction — a high bar.

Only one Cabinet member has been impeached in history — former President Grant’s secretary of war, William Belknap, who was accused of taking kickbacks from a contractor he appointed to run the trader post in Fort Sill, Okla. Belknap resigned before facing an almost-certain Senate conviction, a fate that's unlikely to play out with Mayorkas.

Other Republicans who spoke with The Hill stressed the need to go through the proper oversight channels, rather than leap into impeachment.

House Homeland Security Committee Chairman Mark Green (R-Tenn.), whose panel would be among those with jurisdiction over Mayorkas’s impeachment, was animated when he spoke about the opportunity to remove the DHS chief, pushing their own coming investigation.

“We're going to hold him accountable. That's what we're going to do. We're going to have hearings and dig into what I would say is dereliction of duty,” he said.

“All I can speak about is what we're going to do in the committee and that is a five-phased approach of tackling the fight.”

Rep. Chip Roy (R-Texas) said the GOP needed to handle the matter in “the appropriate way.”

“I've been very public about my belief that he has violated his oath, that he has undermined our ability to defend our country,” he said.

“But I'm on the House Judiciary Committee in the majority now and so I'm going to talk to [Chair] Jim [Jordan] (R-Ohio) and talk to people on that committee to make sure that we're going through this and looking at it in the appropriate way.” 

Rep. Dan Crenshaw (R-Texas), who was initially by McCarthy’s side for the November border trip as he stressed an eventual inquiry, has signed onto Fallon’s resolution as a co-sponsor, saying he believes Cabinet secretaries can be impeached over their policies.

“People argue about this legally, you can impeach a president because you just don't like his policies. In theory that could be considered a high crime or misdemeanor according to the current legal analysis,” he said.

“I just decided I agree with Fallon. That's basically as simple as I can put it.”