House Republicans are planning to plow ahead with their impeachment inquiry into President Joe Biden in the event of a government shutdown, though a lapse in federal funding could present logistical challenges to their investigative work.

In recent days, House Republicans -- like all federal agencies -- have been working behind the scenes to figure out which of their operations and staffers will be deemed "essential" if the government shuts down at midnight on Saturday. And it has been determined that the GOP-led committees heading the Biden impeachment inquiry will fall under that umbrella, according to multiple Republican lawmakers and aides, though formal shutdown plans are still being finalized.

House Oversight Chairman James Comer said a potential shutdown, now just days away, will have no impact on his staff and plans to keep issuing subpoenas, telling CNN on Tuesday, "We're going to keep going."

House Judiciary Chairman Jim Jordan said his staff has been deemed essential and will continue with the steady stream of interviews his panel has lined up, including with top officials at the Department of Justice.

"We've got a number of them scheduled," Jordan told CNN. "Every week there's a whole roster of folks."

Hearings are still allowed to take place even if lawmakers fail to keep the government funded, according to a Republican aide. But it could be tough optics to use government resources to hold public hearings on the GOP's Biden investigations while thousands of federal employees and military personnel aren't receiving paychecks and as things like food stamps and housing assistance start to dry up.

Asked whether Republicans should continue with their impeachment inquiry if the government shuts down, GOP Rep. David Valadao, who represents a California swing district, told CNN: "I'm not even going to waste my time talking about that right now. Right now, I'm focused on the government, keeping it open, and doing what we need to do on that front."

One challenge for House Republicans in moving forward with an impeachment inquiry during a government shutdown is that committees will be seeking information from government agencies where many employees will be furloughed or not prioritizing congressional requests. That means issuing subpoenas and hauling in witnesses for interviews or hearings may prove more complicated than usual.

"We can continue to keep working on the impeachment inquiry, but I think it would affect some of our subpoenas depending on branches that we subpoena information to," GOP Rep. Marjorie Taylor Greene of Georgia, who serves on the Oversight Committee, told CNN.

A source familiar with the executive branch oversight response told CNN, "Agencies are already responding to a flurry of congressional oversight requests with limited resources. A shutdown will exacerbate the problem. Agencies will always do our best to respond to Congress, but the House cannot have their cake and eat it too."

One key decision that has not been determined yet is whether a court reporter, who is responsible for transcribing interviews and depositions, is deemed essential, a source familiar with the process told CNN.

The House Administration Committee is expected to send more formal guidance to offices and committees about what to do during a shutdown at "an appropriate time," according to a source familiar. And Democratic committee staff will be holding a briefing for Democratic member staff on Wednesday about what to expect, a separate source told CNN.

Committee chairmen -- who will have a congressionally mandated salary in a shutdown -- will still have to make key decisions about who on their staff will keep working without pay for the length of the shutdown, with backpay waiting on the other side.

Last week, House Speaker Kevin McCarthy -- in a bid to win over conservative hardliner holdouts who are vowing to oppose a stopgap bill to keep the government's lights on -- warned a potential shutdown would slow down House Republicans efforts to continue to gather information and build their case for the impeaching Biden.

"If the government shuts down it would slow that part, yeah," McCarthy said.

But some of the holdouts were undeterred, and expressed confidence their investigations could continue uninterrupted.

While key logistics are still being worked out, House Judiciary Committee member Mike Johnson did not see an issue with continuing that work during a shutdown.

"I think our responsibility under the Constitution transcends all the politics and the disputes about budgeting and spending and all the rest," he told CNN.