Senior House Republicans are moving swiftly to build a case against Homeland Security Secretary Alejandro Mayorkas as they strongly weigh launching rare impeachment proceedings against a Cabinet secretary, a plan that could generate sharp backlash from GOP moderates.

Key committee chairmen are already preparing to hold hearings on the problems at the southern border, which Republicans say could serve as a prelude to an impeachment inquiry against Mayorkas. Three House committees – Oversight, Homeland Security and Judiciary – will soon hold hearings about the influx of migrants and security concerns at the border.

The House Judiciary Committee, which would have jurisdiction over an impeachment resolution, is prepared to move ahead with formal proceedings if there appears to be a consensus within the GOP conference, according to a GOP source directly familiar with the matter. The first impeachment resolution introduced by House Republicans already has picked up support, including from a member of the GOP leadership team.

A GOP source said the first Judiciary Committee hearing on the border could come later this month or early February.

One top chairman is already sounding supportive of the move, a sign of how the idea of impeaching President Joe Biden’s Cabinet secretary has moved from the fringes to the mainstream of the conference.

“If anybody is a prime candidate for impeachment in this town, it’s Mayorkas,” Rep. James Comer, chairman of the House Oversight Committee, told CNN.

It’s exceedingly rare for a Cabinet secretary to be impeached, something that has only happened once in US history – when William Belknap, the secretary of war, was impeached by the House before being acquitted by the Senate in 1876. Yet it’s a very real possibility now after Kevin McCarthy – as he was pushing for the votes to win the speakership – called on Mayorkas to resign or face potential impeachment proceedings.

With no signs that Mayorkas is stepping aside, House Republicans are signaling they’re prepared to move ahead, even as a bevy of members are uneasy about the approach.

Indeed, McCarthy has to balance his base’s demands for aggressive action with the concerns from more moderate members – many of whom hold seats in swing districts central to his narrow majority. And some in safer seats aren’t yet sold on whether the GOP should pursue that route.

“Clearly, the management of the Southern border has been incompetent,” Rep. Dusty Johnson, a Republican of South Dakota, told CNN. “That is not the threshold in the Constitution for impeachment – it’s high crimes and misdemeanors. … I would want to think about the legal standard the Constitution has set out – and whether or not that’s been met.”

If he loses more than four GOP votes on an impeachment resolution, the effort would fail in the House and could mark a huge embarrassment for the GOP leadership. Already, he has potentially lost one vote – Rep. Tony Gonzales of Texas who signaled he is opposed to the effort right now – and several other members who are far from convinced that charging Mayorkas with committing a high crime and misdemeanor is warranted, even if they believe he’s done a lackluster job in helping secure the southern border.

“Has he been totally dishonest to people? Yes. Has he failed in his job miserably? Yes,” Rep. Mario Diaz-Balart, a Florida Republican, said of Mayorkas. “Are those grounds for impeachment? I don’t know.”

Indeed, Republicans from swing districts are urging their colleagues to not rush into impeachment, which would be dead-on-arrival in the Senate and could turn the American people off if the party is perceived as overreaching.

“The border is a disaster and a total failure by the Biden administration. We should first to try to force change through our power of the purse,” Rep. Don Bacon, who represents a Biden-won district in Nebraska, told CNN. “Maybe after more oversight we’ll see where middle America is at, but I don’t think independent, swing voters are interested in impeachments.”

Asked Tuesday about his pre-election warning that Mayorkas could be impeached by the House over the GOP concerns about the borders, McCarthy railed on the problems at the border.

“Should that person stay in their job? Well, I raised the issue they shouldn’t. The thing that we can do is we can investigate, and then that investigation could lead to an impeachment inquiry,” McCarthy told CNN, adding it could “rise to that occasion” of an impeachment if Mayorkas is found to be “derelict” in his duties.