Speaker Kevin McCarthy in recent weeks has heard similar advice from both a senior House Republican and an influential conservative lawyer: prioritize the impeachment of President Joe Biden over a member of his Cabinet.

Part of the thinking, according to multiple sources familiar with the internal discussions, is that if House Republicans are going to expend precious resources on the politically tricky task of an impeachment, they might as well go after their highest target as opposed to the attorney general or secretary of homeland security.

And McCarthy -- who sources said has also been consulting with former House GOP Speaker Newt Gingrich on the issue -- has warmed up to an idea that has long been relegated to the fringes of his conference. This week, he delivered his most explicit threat yet to Biden, saying their investigations into the Biden family's business deals appear to be rising to the level of an impeachment inquiry.

Speaking to CNN on Tuesday, McCarthy signaled that Republicans have yet to verify the most salacious allegations against Biden, namely that as vice president he engaged in a bribery scheme with a foreign national in order to benefit his son Hunter Biden's career, an allegation the White House furiously denies. But he said that launching an impeachment inquiry would unleash the full power of the House to turn over critical information, mirroring an argument advanced by House Democrats when they impeached then-President Donald Trump in 2019.

"How do you get to the bottom of the truth? The only way Congress can do that is go to an impeachment inquiry," McCarthy said Tuesday, stopping short of formally moving to open such a probe.

It all amounts to a consequential shift in thinking among Republican leaders, who were previously reluctant to call for Biden's impeachment and have instead focused more energy on Homeland Security Secretary Alejandro Mayorkas and Attorney General Merrick Garland. Those were largely seen as lower stakes fights that could be easier to sell to the party and the public.

Yet as some of the GOP's investigative lines have lost momentum -- border crossings are down in recent weeks, for example -- and Republicans believe they have uncovered compelling new information about Hunter Biden, they increasingly see the president as their most ripe candidate for impeachment.

"There is clearly a greater chance of convincing people and more importantly senators that Biden himself committed a high crime than Mayorkas," a senior House GOP member told CNN.

As another senior GOP source put it: "When you're going deer hunting, you don't shoot geese in the sky."

Even some of the more hardline members of McCarthy's conference said that if the GOP needs to settle on one target, it should be Joe Biden.

"If I had to pick one, I would pick Biden," said Rep. Andy Ogles, a Tennessee Republican and member of the House Freedom Caucus.

The White House has maintained that Biden has had no involvement in his son's business deals, and Republicans have yet to link Biden directly to them.

But even with more Republicans coalescing around the idea, impeachment would still be a complicated and time consuming endeavor, given McCarthy's razor thin majority and the need to fund the government by September 30. And there's anxiety about impeachment backfiring with the party's moderates while energizing the Democratic base, all for an effort that is sure to be doomed in the Senate -- a similar concern shared by Democrats in 2019, when they launched their first impeachment into Trump ahead of the 2020 election, proceedings that took about three months to complete in the House.

In moving to potentially make Biden just the fourth president in US history to get impeached, McCarthy could appease some of his sharpest critics in his conference, especially as the House will have to cut a deal in the fall to keep the government funded and prevent a shutdown. Some on his far-right, who have threatened to boot him from the speakership if he strays from their demands, are now praising his embrace of potential impeachment proceedings.

"We probably should have moved to an impeachment inquiry probably sooner than this," said Arizona Rep. Andy Biggs, a former leader of the House Freedom Caucus. But he added: "I understand."

"He was reticent at first," Biggs said of McCarthy. "We don't want to look like our colleagues across the aisle. But as we've continued to amass evidence and information, I certainly think (at) a bare minimum, we should be doing an impeachment inquiry."

Rep. Bob Good, a Virginia Republican who tried to prevent McCarthy from winning the speakership, said of McCarthy: "I don't there's any question that him speaking to that has caused a paradigm shift."

"I'm just glad to hear that the speaker is recognizing that that we need to follow the evidence and the truth wherever it might lead us," Good said. "I don't know how anyone, any objective, reasonable person couldn't come to the conclusion that this appears to be impeachment worthy."

But GOP Rep. Ken Buck of Colorado, a member of the Judiciary Committee and hardline Freedom Caucus who has been more skeptical of impeachment, shot back at the idea he would take impeachment cues from the speaker: "The Freedom Caucus hasn't listened to McCarthy in years."

"I can't imagine that we would start now," he told CNN.

'I couldn't prioritize one'

With concerns among vulnerable members that impeaching Biden may not be a winning message in their districts, House Republicans would like to wrap up any such proceedings before year's end, according to senior Republican sources familiar with the party's thinking. But that means Republicans are going to have to make a decision soon on if -- and whom -- they want to impeach, given the desire among Republicans for impeachment hearings and a formal inquiry process. The House is slated to leave at the end of this week for a six-week recess.

Getting an impeachment resolution through the narrowly divided House -- where McCarthy can lose no more than four of his members on party-line votes -- will only get tougher in an election year, Republicans say.

Plus Republicans still appear to be all over the map on their impeachment strategy.

Firebrand Rep. Marjorie Taylor Greene, a Georgia Republican who is not only seeking to expunge Trump's two impeachments but also introduced a slew of impeachment articles against Biden and members of his Cabinet, told CNN: "I couldn't prioritize one."

That sentiment was echoed by Rep. Ralph Norman, a hard-right South Carolina Republican who said impeaching Biden is just "the start of the list."

"His judgment is wrong on who he has in office," Norman said. "They got to have to be accountable. And I think you're seeing the accountability now."

But with economic concerns expected to dominate voters' minds in next year's elections, many in the House GOP have been skeptical about moving forward with charging the president with committing a high crime or misdemeanor.

Nebraska GOP Rep. Don Bacon, whose district Biden carried in 2020, told CNN that the House needs to be deliberate.

"This needs to be thoroughly vetted in the Judiciary Committee," Bacon said, arguing the approach needs to differ from the two impeachments under then-Speaker Nancy Pelosi.

"The Watergate profile is what we should benchmark off of, not the Pelosi method of putting it on the floor without a single committee hearing," Bacon said. "Pelosi watered down and lowered the threshold for impeachment, and we should not follow her example. It's not good for the country."

In the first Trump impeachment, House Democrats led a number of closed and open hearings before charging Trump with abuse of power and obstructing Congress. In the second impeachment, Democrats charged Trump with inciting the January 6, 2021, insurrection just days after the deadly attack in the Capitol.

Republicans have already had a tough time convincing even members of the House Judiciary Committee, where impeachment articles would originate. Indeed, one GOP Judiciary member who has been skeptical of a Mayorkas impeachment leaned over to share that assessment with a Democrat on the panel during a recent hearing.

Democrats say Republicans are just using the threat of impeachment as a political stunt to help boost Trump, who remains their frontrunner in the GOP presidential primary.

"It's clear that Donald Trump is the real Speaker of the House," Jaime Harrison, chair of the Democratic National Party, said in a statement. "He has made sure the House majority is little more than an arm of his 2024 campaign, and Kevin McCarthy is happy to do his bidding."

Indeed, McCarthy has been under pressure to placate Trump, particularly after he questioned Trump's strength as a candidate -- comments he quickly walked back. As CNN previously reported, McCarthy told Trump in a private phone call that he supports the idea of expunging his past two impeachments and said he would bring the idea up with the rest of the conference.

But there's no sign that GOP leadership is planning to bring such a symbolic resolution to the floor any time soon, with many Republicans pouring cold water on the idea. That has privately frustrated Trump, who called Greene earlier this month to complain about the lack of action from McCarthy, according to a source familiar with the conversation.

McCarthy has had to walk a tightrope on the issue of impeachment amid growing frustration from his right flank, which has been itching to launch impeachment proceedings. Last month, McCarthy opted to defer a push from GOP Rep. Lauren Boebert of Colorado to force a snap floor vote on impeaching Biden over his handling of the southern border and immigration problems, saying they need time to gather the facts and build a case.

On Tuesday, Boebert took notice of the apparent shift in McCarthy's tone.

"The Speaker of the House is now talking impeachment," Boebert tweeted. "The Biden corruption has risen to a level that there is no other response that can possibly be leveled against it. Impeachment is a very big deal, but these are incredibly serious crimes. I look forward to holding Joe Biden accountable for all that he's done."

Hunter Biden probe moves front and center

Republicans argue that a string of recent developments have generated new momentum that has helped bring McCarthy on board and will even satisfy the remaining holdouts.

Last week, GOP Sen. Chuck Grassley of Iowa released an internal FBI document containing unverified allegations that both Hunter and Joe Biden were involved in an illegal foreign bribery scheme that Republicans had been trying to make public for weeks, despite serious warnings from the FBI.

The House Oversight Committee held a hearing last week that put a spotlight on two IRS whistleblowers who have claimed that the Justice Department politicized the Hunter Biden criminal probe, and has a deposition with Hunter Biden's long-time associate and Burisma co-board member Devon Archer next week. And the House Judiciary Committee just secured assurance from the Justice Department that US Attorney David Weiss, who is overseeing the Hunter Biden criminal probe, can testify publicly before Congress this fall.

But Republicans still have yet to tie such allegations directly to the president's actions, which will be a major hurdle for GOP leaders to clear if they move ahead with impeaching Biden. The White House has repeatedly stated that the allegations launched by Republicans have all been debunked.

Part of the consideration for House Republicans will be figuring out how to delineate or combine the work currently being conducted by House Oversight Chair James Comer and House Judiciary Chairman Jim Jordan, who are in constant communication with each other and McCarthy, sources told CNN.

With just three days to go before the House stands in recess for six weeks, Greene, who continues to serve as a conduit to Trump in the House and has been relentless in pushing McCarthy toward a Biden impeachment, wasted no time in making her case again on the House floor.

And afterward, the firebrand conservative had this message to her reluctant GOP colleagues: "Any Republican that can't move forward on impeachment with all of the information and overwhelming evidence that we have, I really don't know why they're here to be honest with you."