House conservatives want their party to go big on impeachment next year. Across the Capitol, Senate Republicans on their would-be jury are not ready to convict.

While House GOP leaders feel intense pressure from their Donald Trump-aligned base and colleagues to impeach President Joe Biden or a top member of his Cabinet, many of the party’s senators want nothing to do with it. In fact, some Republican senators are openly signaling that even if impeachment managed to squeak through the House, it would quickly die in their chamber — and not just at the hands of the Democratic majority.

Sen. John Cornyn (R-Texas), a close ally of Minority Leader Mitch McConnell, said he “hadn’t really given any thought” to impeaching Biden or a Cabinet official like Department of Homeland Security Secretary Alejandro Mayorkas, whom Kevin McCarthy singled out last month as a primary target of future House investigations. Cornyn said he hasn’t seen any actions that meet the bar for an impeachable offense: “Not really, no.”

And Utah Sen. Mitt Romney, the only GOP senator to twice convict former President Trump, put it more bluntly: “Someone has to commit a high crime or misdemeanor for that to be a valid inquiry. I haven’t seen any accusation of that nature whatsoever. There are a lot of things I disagree with … but that doesn’t rise to impeachment.”

Cooling their counterparts’ impeachment fever is just one of many tricky tasks facing the Senate GOP over the next two years in its relationship with an incoming House majority where pro-Trump conservatives often shout the loudest. While those House Republicans look to ding Biden’s administration after six years trapped in the minority, the party’s senators are picking battles more carefully.

A big reason behind the different strategies: House Republicans will hold the party’s biggest megaphone on Capitol Hill heading into 2024, with some of their own GOP centrists already feeling heartburn — and hearing Democratic warnings — that pursuing impeachment will backfire in the next election.

Sen. John Thune (R-S.D.), McConnell’s No. 2, subtly urged House Republicans to focus on specific investigative targets that could help the party put pressure on Democrats. He added that the border was a “debacle” and that Mayorkas should be called in for “oversight,” but underscored that what specific actions should spin out of such investigations was not yet clear.

“I think there is a legitimate need for oversight … but, I mean, I think it needs to be focused on some specific areas,” Thune said. When asked about the possibility of impeaching Biden himself, Thune repeated that they should outline certain investigative targets and “see if we can’t pressure the Democrats into working with us on a few things.”

It’s an ongoing pattern for Republican Senate leaders, who have mostly tried to avoid the pitfalls of Trump-related probes. While House GOP leadership has leaned hard into publicly pushing back on the Democratic-run panel investigating the Jan. 6 attack on the Capitol, their Senate counterparts have largely sidestepped tangling with the select committee.

Meanwhile, McCarthy called on Mayorkas to resign or face possible impeachment during a trip to the border last month. The Californian first opened the door to impeaching the Homeland Security secretary earlier this year, and his most recent remarks dovetail with his efforts to lock down support from conservatives who have threatened to oppose his speakership bid.

Rep. Andy Biggs (R-Ariz.), who lost to McCarthy for the conference’s speakership nomination last month, has introduced a resolution to impeach Mayorkas that’s supported by several of the minority leader’s most vocal critics.

Spokespeople for McConnell, who teed off on the administration’s border policy from the floor Monday, didn’t respond to a question about impeaching Mayorkas. The GOP leader also quashed calls to impeach Biden last year that were sparked by a widely criticized Afghanistan withdrawal.

Because Senate Republicans will be stuck in the minority for at least the next two years, they can’t do much to contribute to House GOP investigations. And for some GOP senators, questions about their counterparts’ impeachment dreams elicit responses that put a new spin on M.C. Hammer’s 1990 hit: They can’t, and won’t, touch this.

Maine Sen. Susan Collins, one of the seven Republican senators who voted to convict Trump last year, said with a laugh that she was “not going to get into the machinations of the House.”

“That’s not something I’ve heard discussed over here,” Collins said about impeaching Biden or Mayorkas.

And Iowa Sen. Chuck Grassley, the top Republican on the Judiciary Committee, brushed off questions about if he supports a Biden or Mayorkas impeachment: “I can’t do anything about what the House does.”

It was always a long shot that the Senate would convict in any impeachment trial next Congress, given it would require 67 votes in favor. No presidents have been found guilty and the one Cabinet official who was the subject of an impeachment trial was acquitted. But House Republicans’ roughly five-seat margin next year means that dreams of even passing an impeachment of Biden or his top lieutenants through their own chamber might have already died on the vine.

Still, the staunchest pro-impeachment House Republicans aren’t deterred by the reality that their efforts would ultimately fail across the Capitol — or even alienate some in their own party. They see it as their business to take on the Biden administration, and winning the majority means business is about to pick up.

“I would say back to them: ‘Then why enforce any laws? Why do anything?’ I think we always have to hold people accountable. We have to do our job in the House, regardless of what is going to happen in the Senate,” said Rep. Marjorie Taylor Greene (R-Ga.), who has pushed impeaching Biden since he took office.

And Greene’s camp does have some Senate Republicans in its corner when it comes to impeaching Mayorkas. Sens. Ted Cruz (R-Texas) and Lindsey Graham (R-S.C.), who was an impeachment manager against former President Bill Clinton, sent a letter to Mayorkas arguing that his actions, if not corrected, could provide “grounds for impeachment.”

In addition, Sen. Josh Hawley (R-Mo.) accused Mayorkas of having “misled” him and members of the Homeland Security and Governmental Affairs Committee and being “unresponsive.” He added in a brief interview that “I think an impeachment there is probably warranted” and could be used to get information from the agency.

But asked about the prospect of impeaching Biden, Hawley, who has disavowed any interest in a run of his own in two years, pointed to the 2024 election as the better venue.

“You know, I’m not a fan of the president. … But impeaching a president is a very, very, very high bar,” he said. “The American people, pretty soon here, are going to have a chance to weigh in again.”

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