Facing the prospect of a politically damaging authorities shutdown inside weeks, House Speaker Kevin McCarthy is providing a brand new argument to conservatives reluctant to vote to maintain funding flowing: A shutdown would make it harder for Republicans to pursue an impeachment inquiry in opposition to President Biden, or to push ahead with investigations of him and his household that might yield proof for one.

Mr. McCarthy first made the case on Sunday throughout an interview on Fox News by which he warned {that a} shutdown would stall the House’s ongoing inquiries into the president and his household. His argument mirrored the speaker’s rising desperation to discover a method to persuade right-wing Republicans to drop their opposition to a stopgap measure that’s wanted to maintain federal cash flowing past the Sept. 30 finish of the fiscal 12 months.

By tying the problem to the prospect of impeaching Mr. Biden, Mr. McCarthy seems to be hoping that the conservative want to research and probably cost him with excessive crimes and misdemeanors — significantly amid the a number of legal instances in opposition to former President Donald J. Trump — may outweigh their resistance to voting in favor of federal spending.

“If we shut down, all the government shuts it down — investigation and everything else,” Mr. McCarthy mentioned concerning the prospect of funding operating out Sept. 30. “It hurts the American public.”

In the interview, he known as impeachment a “natural step forward” from the various inquiries Republicans have pursued in opposition to the president, however he sidestepped a query about whether or not he had the votes to take action given the deep divisions amongst G.O.P. lawmakers about such a course.

Allies of Mr. McCarthy say that persevering with the investigations throughout a shutdown wouldn’t solely violate legal guidelines prohibiting Congress from partaking in unauthorized spending, it will current a politically charged spectacle of the House holding investigatory hearings whereas 1000’s of presidency staff are furloughed and businesses shuttered.

But among the conservatives Mr. McCarthy would wish to cooperate have rejected the speaker’s attraction, saying that Republicans on Capitol Hill may stick with their inquiries even when different elements of the federal government have been closed.

“It’s not as if the investigators won’t be considered necessary or essential personnel,” mentioned Representative Ken Buck, Republican of Colorado, who famous that as speaker, Mr. McCarthy would have authority to find out which elements of the House proceed to function. “He is the one who decides how much of the House we shut down.”

Representative Matt Rosendale, Republican of Montana and Mr. Buck’s fellow member of the hard-right Freedom Caucus, additionally dismissed the concept that the arch-conservative Republicans insisting on deeper reductions in spending can be persuaded to relent by the specter of slowing the inquiries.

“We are not going to be distracted by shiny objects, saying if you don’t get this continuing resolution passed, we won’t be able to pursue the impeachment inquiry,” Mr. Rosendale mentioned in a Monday interview on Fox News. “That’s nonsense.”

Mr. McCarthy’s place and its rejection by among the most conservative members of the House illustrates the predicament he’s in because the spending combat begins in earnest with the return of the House and Senate in September.

Multiple conservatives have indicated they aren’t keen to entertain even a short-term extension to supply extra time to contemplate the yearlong spending measures with out quick concessions comparable to deeper spending cuts, eliminating funding for the prosecution of Mr. Trump and inflexible border controls.

A number of have brazenly embraced the thought of a shutdown. With solely 4 votes to spare, Mr. McCarthy may flip to Democrats for assist in funding the federal government as he did in elevating the debt ceiling in May, however that will be all however sure to create a backlash from his personal celebration. And Democrats could have calls for of their very own; they already object to lots of the coverage provisions being pursued by Republicans.

Representative Hakeem Jeffries of New York, the Democratic chief, mentioned in a CNN interview on Tuesday that he had but to debate the prospects for a stopgap invoice with Mr. McCarthy.

“I do expect that at some point in time, within the next week or so, we’ll begin to intensify those conversations,” he mentioned, including that retaining the federal government working was “our fundamental responsibility.”

Mr. McCarthy and Senator Chuck Schumer, the New York Democrat and majority chief, have mentioned they agree {that a} “continuing resolution” sustaining funding shall be wanted to maintain the federal government open after Sept. 30.

The House has handed simply one among its 12 spending payments, and conservatives are threatening to sink among the others with out deeper spending cuts and added provisions comparable to denying funding for Trump prosecutions. The Senate has not but put any of its appropriations payments on the ground, although the Appropriations Committee has authorized all 12 on a bipartisan foundation at larger spending ranges than the House, establishing a conflict.

Allies of Mr. McCarthy mentioned his warning that the investigations can be halted relies on the federal Anti-Deficiency Act, which prohibits federal agencies and employees from spending in advance or in excess of appropriations. Individual workers members could be subjected to penalties in the event that they violate it.

The allies say hearings might be held solely in uncommon instances, no subpoenas might be issued or depositions taken and solely staff important to reopening the federal government may report back to work.

At the identical time, congressional officers famous that the federal prosecutions of Mr. Trump may proceed even when the remainder of the federal government was closed since legal issues have prior to now been thought of exempt from shutdowns.

In a 2021 memo, the Justice Department mentioned that in a shutdown, “criminal litigation will continue without interruption as an activity essential to the safety of human life and the protection of property.” Moreover, particular counsel investigations, together with the inquiry into Mr. Trump, are funded through a “permanent, indefinite appropriation for independent counsels.”