Republicans have vowed to use the full power of the House of Representatives if they take control in November, threatening everything from shutting down investigations into the Jan. 6 riot at the Capitol to impeaching President Biden and his cabinet secretaries.

While Republicans are all but certain to terminate the select committee on the Jan. 6 attack, it's less clear whether they'll risk the political uncertainties of an impeachment trial.

But if they take the plunge, their sights will be on Homeland Security Secretary Alejandro Mayorkas.

In a letter to Mayorkas last week, GOP Sens. Lindsey Graham (S.C.) and Ted Cruz (Texas) explicitly threatened impeachment over the secretary's "gross dereliction of duty" in managing the U.S.-Mexico border.

That missive followed an April letter led by the Republican Study Committee and signed by 133 House Republicans that avoided explicitly calling for impeachment, but laid out the case for Republicans to raise immigration policy differences to the level of impeachable offenses.

"Your actions have willingly endangered American citizens and undermined the rule of law and our nation's sovereignty. Your failure to secure the border and enforce the laws passed by Congress raises grave questions about your suitability for office," wrote the lawmakers.

The Constitution allows for impeachment of the president and other “civil officers” for “treason, bribery, or other high crimes and misdemeanors."

But it's unclear what is meant by "high crimes and misdemeanors," and impeachment is understood to be an essentially political act – a Senate would need very little substantial cause to convict an official impeached by the House.

"With my political scientist hat on, I'd say what counts as a high crime or misdemeanor is what you can get two thirds of the Senate to vote to convict on. And that in itself, it's not a substantive standard. It's a procedural one," said Josh Chafetz, a professor of law at Georgetown University.

But Chafetz added that's a "very high bar," since it would require significant buy-in from the president's party.

And while technically there are no limits – other than whip counts in both chambers – to what behaviors Congress can interpret as "high crimes and misdemeanors," precedent does set some boundaries.

“The Constitution provides for impeachment in the case of treason, bribery, or other high crimes and misdemeanors — not for political revenge or partisan retribution," said David Rapallo, director of the Federal Legislation Clinic at Georgetown Law.

That reading still leaves space for debate as to what constitutes grounds for conviction under impeachment.

"There's been a debate about whether there must be a statutory code violation of a crime to impeach. The general view is that it doesn't necessarily have to be a criminal act under the statutory code, but rather an abuse of power in some way,” said Rapallo.

The Republican case against Mayorkas lies largely on high migrant apprehension and drug interdiction numbers at the southwest border.

U.S. officials encountered 2,150,639 immigrants entering the country without prior authorization in the first 11 months of fiscal 2022, breaking the record for encounters in a year.

And fentanyl seizures continue to rise, as Mexican drug cartels abandon other drugs for the cheaper-to-produce synthetic opioid.

If the GOP takes control of the House, they will almost certainly bring down the hammer on Mayorkas through congressional oversight, but Republicans seem eager to raise the specter of impeachment.

In their letter, Graham and Cruz accuse Mayorkas of aggravating conditions on the border, in part by attempting to end policies put in place under the Trump administration, namely construction of the border wall; the Migrant Protection Protocols (MPP), better known as "Remain in Mexico"; and Title 42, a policy to quickly expel foreign nationals under the guise of pandemic protections.

While the Department of Homeland Security halted border wall construction shortly after Biden took office, Customs and Border Protection (CBP) officials announced a plan to return to construction sites in the Sonoran Desert to resume construction of some segments of the wall.

But Graham and Cruz zeroed in on Mayorkas' attempts to end MPP, which are tangled up in the courts.

"Your expedited and repeated rejection of President Trump's successful Migrant Protection Protocols … demonstrates your willingness to embrace an open-borders agenda that undermines America's safety," they wrote. 

"You have been specifically instructed by the court to implement the protocol in good faith or take new agency action that complied with the law. You have done neither."

While the Biden administration was originally directed by the 5th Circuit Court of Appeals to continue MPP's implementation "in good faith," the case was returned to a lower court after the Supreme Court sided with the Biden administration's plans to end the policy.

A lower court lifted the order to continue implementing MPP and DHS has been winding the program down.

"In short, MPP is over for now, although there is confusion surrounding its ending," reads a post on MPP's current state of affairs on the American Immigration Lawyers Association blog.

That distinction could blunt the GOP senators' call for impeachment.

"The traditional story we tell about impeachment in America is that it doesn't apply to just bad policy. It's not about maladministration, but rather, it's about malfeasance or nonfeasance," said Chafetz.

And historical precedent is on cabinet members' side when it comes to impeachment.

The only cabinet member ever impeached was 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, Oklahoma.

While most historians agree the accusations against Belknap were credible, he avoided conviction in his 1876 impeachment trial because he resigned on the same day he was impeached.

Like President Nixon nearly a century later, Belknap chose to resign rather than face almost certain conviction in the Senate, although the House did pass Belknap's articles of impeachment.

“If it were something like Richard Nixon — that era where his own party was telling him what was coming, and it would be better for him to resign than go through that process — he chose to resign, and after that occurred, they didn't go forward,” said Rapallo.

The precedent that being out of office obviates an impeachment conviction was reinforced in 2021, when Trump was acquitted in his second impeachment trial after leaving office.

Because of that precedent, any official facing probable impeachment conviction is more likely to resign than to become the first executive officer convicted by the Senate.

"​​​​I just don't see any way they would get to 67 [Senate votes] based on what we've seen now," said Chafetz.

"Now, again, if it turns out tomorrow that some member of the cabinet has a freezer full of cash that they got from a foreign government, sure. But of course in that situation, they'd almost certainly resign or be fired," he added.

Conversely, Biden and his cabinet are unlikely to yield in an impeachment trial they can win, even if the proceedings disrupt an official's duties.

"If you're Biden, it's a short term-long term trade off, because maybe the department can get a move on with business, but the Republicans have successfully claimed a scalp and what's to prevent them from going after the next cabinet official?" said Chafetz.

And if Republicans do take the House, their leadership ranks will have their hands full controlling an ideological and outspoken caucus.

While at least two separate articles of impeachment have been filed against Biden by Republican lawmakers in the current Congress, GOP leadership has not invested political capital in those bills.

Any GOP impeachment of Biden risks being seen as a tit-for-tat over the two Democratic impeachments of Trump, and that protection could extend to cabinet secretaries.

“The Constitution doesn't provide for impeaching a cabinet secretary because you think impeaching the president is too much politically,” said Rapallo.

And dragging immigration into a constitutional controversy could backfire for Republicans.

“It's well known that the Republicans were close to agreeing on legislation related to immigration, but changed their minds and haven't been interested in solving the problem since then,” said Rapallo.

“So on one hand, to walk away from the effort to legislate, and then on the other, to go after the cabinet secretary who's charged with implementing the laws is a little rich, I would say.”