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(CNN)A growing number of Republicans are openly cheering for a competitive primary field in 2024 and encouraging candidates to jump into the race, as some in the GOP get increasingly anxious about the idea of Donald Trump becoming their presidential nominee again -- especially amid damning revelations about his actions during the January 6, 2021, insurrection.

Rep. Dan Crenshaw, a member of the conservative Republican Study Committee, said that the party has a "lot of good options" and he hopes "they all jump in" to the race. The Texas Republican added that he does not think Trump would be the automatic frontrunner if he decides to launch a third White House bid.

Senate Minority Whip John Thune told CNN that there will be "other attractive" Republican candidates in 2024 besides Trump, echoing recent comments from Senate Minority Leader Mitch McConnell, who predicted it will be a crowded field.

And Rep. Dusty Johnson, a South Dakota Republican and member of the bipartisan Problem Solvers Caucus, said he thinks it would be healthy for the GOP to have a debate about who should be their next standard-bearer.

"I certainly hope we'll have a crowded field so we can have a robust discussion," Johnson told CNN. "Trump's going to have a certain amount of built-in support. So yeah, he's gonna be ahead in early polls. But I also know that these primaries hardly ever go as scripted."

"So that's why you gotta let the process play out," he added.

While Trump still maintains more support among Republicans than any other would-be challenger, there are growing fears inside the GOP about Trump's potential legal woes and political baggage, which has some lawmakers eying the party's bench of alternative options, according to Republicans granted anonymity to speak more freely. There is particular concern in GOP circles about the criminal investigation out of the Fulton County District Attorney's office, which is probing the plot by Trump and his allies to appoint false electors in Georgia in an attempt to overturn the 2020 election results.

As Crenshaw put it: it would "suck" to select a GOP nominee that winds up getting indicted, though he said he is making no predictions about the outcome of those investigations.

"I won't be supporting Donald Trump for president or anything else," said Sen. Mitt Romney of Utah, a leading anti-Trump voice in the GOP who voted to convict Trump in both of his impeachment trials. "I think he's hurt our party and I think he continues to do so."

Still, most Republicans -- even those who are apprehensive about another Trump bid -- are signaling they'd fall in line if he ultimately throws his hat into the ring and prevails in the primary.

"It's always been my practice to support the nominee," Thune said when asked if he would back Trump as the GOP nominee even if he questioned his fitness for office.

As the House select committee investigating the January 6 insurrection has publicly revealed damaging details about Trump's role in the Capitol attack, the former President has begun to weigh an early White House bid -- potentially even before the midterms -- in an effort to both freeze the field and shift the narrative. His fiercest allies have welcomed the idea of another Trump run.

"Speaker Pelosi's January 6th Committee is nothing more than a partisan sham. The American people see right through it," House GOP Conference Chair Elise Stefanik said in a statement to CNN. "I strongly support President Trump, and hope he runs again in 2024. And if the election were held today, there is no question he would beat Joe Biden handily."

Even with the threat of Trump running again, a number of Republicans have begun to explore potential presidential bids and meet with donors. Some of them have not ruled out directly challenging Trump for the nomination if he decides to get in the race.

Rep. Austin Scott, a Georgia Republican and member of the RSC, told CNN he thinks it would be "great" to see multiple candidates compete for the party nomination, noting that while he would "probably" back Trump, he is also friends with Florida Gov. Ron DeSantis and former Secretary of State Mike Pompeo -- both former House members.

Rep. Dan Newhouse of Washington, one of 10 House Republicans who voted to impeach Trump for inciting the insurrection, agreed, saying they ought to see "who has all the best ideas."

2024 hopefuls get a stage on Capitol Hill

The Republican Study Committee, the largest conservative caucus on Capitol Hill, has hosted a number of these 2024 hopefuls over the past year -- including Pompeo, Sen. Tom Cotton of Arkansas, and former South Carolina Gov. Nikki Haley -- and offered them a platform to share their vision and build congressional alliances. The group has also met numerous times with Trump.

Most recently, the group met with former Vice President Mike Pence, who telegraphed in several high-profile moves last week that he is actively exploring a 2024 presidential bid and working to gain a foothold in Trump-fatigued corners of the Republican Party.

"That's what has made the RSC important, is that we've been planting the flag for where the party goes from here," Rep. Jim Banks, a fellow Indiana Republican who chairs the Republican Study Committee, told CNN. "The RSC has always believed that if we adopt the Trump agenda as our party platform, then our party will be stronger and healthier than ever before."

During a closed-door meeting with the RSC on Wednesday, some members thanked Pence for his actions on January 6 -- when he oversaw the certification of the 2020 election results -- and others encouraged him to run for president in 2024, according to attendees.

"I'm a fan of (Pence's). I'm not here to push him one way or the other way," said Rep. Don Bacon, a Nebraska Republican. "But I like his character."

GOP Rep. Greg Pence of Indiana said he hopes his brother decides to mount a bid for president and would support him "100%" if he did.

When asked whether Pence sounded like someone with their eyes on the Oval Office, Johnson responded: "Anytime anybody who is not a sitting member of the House or Senate comes to DC and gives a speech, I think it's a pretty fair assumption that they have at least some interest."

Banks has previously identified himself as an early supporter of a potential Pence 2024 campaign if Trump were to sit on the sidelines in the next election cycle. But Banks, who has emerged as one of Trump's staunchest supporters on Capitol Hill and may be wary of seeming too supportive of one of Trump's potential 2024 rivals, predicted on Wednesday Trump would clear the field and go on to win the White House if he decides to run.

"If Donald Trump doesn't run for president in '24, then we have the best field we've ever had," Banks said. "If Donald Trump does run, I think he clears the field, he's the nominee and I think he wins in a landslide in November 2024."

Others, however, may have a more difficult time choosing sides in a packed primary. Rep. Brian Mast, a Florida Republican, told CNN he would support Trump if he announced a presidential run right now. But he also said the same of DeSantis.

"It's hard to play it out, because neither of them are stepping out" at the moment, Mast told CNN. "But in a hypothetical of things, both of them have my support."

Some Republicans dodged questions about 2024, saying they were focused on the upcoming midterms.

"I'm not going to get involved in the presidential primary," said Sen. John Cornyn of Texas, a member of GOP leadership.

"I'm not going to worry about the presidential election until we get well into the Iowa caucus," added Sen. Chuck Grassley, an Iowa Republican. "But anybody that wants to run for president is going to have to compete for it."

CNN's Ted Barrett contributed to this report.