Centrist Republicans on Wednesday moved one signature closer to forcing immigration votes on the House floor, but encountered headwinds as some Republicans fretted about the possibility of retribution from leadership.

Rep. Erik Paulsen Erik Philip PaulsenMinnesota Rep. Dean Phillips wins primary Pass USMCA Coalition drops stance on passing USMCA Two swing-district Democrats raise impeachment calls after whistleblower reports MORE (Minn.) on Wednesday became the latest Republican to add his name to the petition, leaving the centrists just a few signatures short of being able to trigger the votes.

But it remains to be seen whether several Republicans who are sympathetic toward the discharge petition will defy leadership and sign on. Some of those lawmakers have told the petition leaders they are concerned about being punished if they back the insurgent effort, according to a Republican aide familiar with the conversations.

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Rep. Mark Amodei Mark Eugene AmodeiBipartisan lawmakers call for Postal Service relief Mnuchin details IRS challenges with cash-only marijuana businesses On The Trail: Democrats plan to hammer Trump on Social Security, Medicare MORE (R-Nev.), who signed the petition, said he has heard similar concerns from colleagues.

“That’s the card that’s being played right now,” Amodei told The Hill.

“I think they’re facing pressure not to sign it,” Amodei added, pointing to Reps. Brian Fitzpatrick Brian K. FitzpatrickFlorida Democrat introduces bill to recognize Puerto Rico statehood referendum DCCC reserves new ad buys in competitive districts, adds new members to 'Red to Blue' program 2020 Global Tiger Day comes with good news, but Congress still has work to do MORE (R-Pa.) and Rep. Dan Newhouse Daniel (Dan) Milton NewhouseThe Hill's Coronavirus Report: Rep. Khanna says President Trump threatening violence against US citizens; Trump terminating relationship with WHO GOP lawmaker introduces bipartisan guest worker bill Overnight Energy: Murkowski, Manchin unveil major energy bill | Lawmakers grill EPA chief over push to slash agency's budget | GOP lawmaker accuses Trump officials of 'playing politics' over Yucca Mountain MORE (R-Wash.). “It’s no secret the Speaker doesn’t want a discharge petition.”

Further underscoring their fears, Rep. Austin Scott James (Austin) Austin ScottMaybe they just don't like cowboys: The president is successful, some just don't like his style Lobbying world Lawmakers warn Pentagon against reduction of US forces in Africa MORE (R-Ga.) stood up during a GOP conference meeting on Tuesday morning and called on leadership to punish lawmakers who sign the petition or who vote against rules setting up floor debate for other immigration bills, according to two Republican sources.

“After leadership presentations, somebody gets up and says, ‘There ought to be discipline … for people who vote against rules, for discharge petitions. How could these people be committee chairs and stuff like that?’” said one Republican lawmaker in attendance.

“Leadership did not comment,” the lawmaker added.

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Speaker Paul Ryan Paul Davis RyanKenosha will be a good bellwether in 2020 At indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates MORE (R-Wis.) is not known to use the same strong-arm tactics as his predecessor, John Boehner John Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE (R-Ohio). And many Republicans who have held off on signing the petition say they are giving leadership some breathing room to broker a deal.

Rep. Dennis Ross Dennis Alan RossRep. Ross Spano loses Florida GOP primary amid campaign finance scrutiny Israelis and Palestinians must realize that each needs to give, not just take Court opens door to annexing the West Bank — and the consequences could be disastrous MORE (R-Fla.), a senior member of the GOP whip team, pointed out that Paulsen, the latest Republican to sign the petition, is roommates with Majority Whip Steve Scalise Stephen (Steve) Joseph ScaliseHouse GOP slated to unveil agenda ahead of election House panel details 'serious' concerns around Florida, Georgia, Texas, Wisconsin elections Scalise hit with ethics complaint over doctored Barkan video MORE (R-La.).

Still, the growing concern over retribution comes as the petition is just four Republican signatures shy of succeeding, assuming all Democrats sign on. Paulsen, a top Democratic target in the midterm elections, became the 21st Republican to sign the petition on Wednesday.

Supporters of the effort continue to express confidence that they will be able to clinch the necessary signatures to force immigration votes if Republican leaders can’t work out a deal.

“We absolutely positively have them. We’ll be ready to go on [June 7] if this falls through,” Rep. John Katko John Michael KatkoThis week: House returns for pre-election sprint Hillicon Valley: Simulated cyberattack success | New bill for election security funding | Amazon could be liable for defective products Lawmakers introduce bill to help election officials address cyber vulnerabilities MORE (R-N.Y.) told reporters on Wednesday, referring to the date of a GOP conference meeting on immigration.

Ryan and his top lieutenants are feverishly working to quash the petition, warning it will hand control of the floor to Democrats. They have been meeting with both moderates and conservatives to hash out an alternative agreement allowing immigration votes on the floor.

Centrists don’t usually play hardball with leadership, but they are employing aggressive tactics after growing increasingly frustrated with the lack of action.

They are seeking a permanent solution for the Obama-era Deferred Action for Childhood Arrivals (DACA) program, which provides protection from deportation for young immigrants who came to the country as children. President Trump announced he was ending the program last year.

However, it’s unclear how far the moderate Republicans are willing to go in their quest to force immigration votes. Unlike the far-right House Freedom Caucus, which has long been a thorn in the side of leadership for years, many of the petition signers or would-be signers are close to leadership and don’t typically rock the boat.

In addition to the petition, the centrists are also threatening to torpedo a rule that would bring a conservative immigration bill from House Judiciary Committee Chairman Bob Goodlatte (R-Va.) to the floor, unless they also get a guaranteed vote on moderate immigration legislation.

Freedom Caucus Chairman Mark Meadows Mark Randall MeadowsHouse moves toward spending vote after bipartisan talks House Democrats mull delay on spending bill vote Southwest Airlines, unions call for six-month extension of government aid MORE (R-N.C.), who has called on leadership to do everything in their power to stop the discharge petition from moving forward, pointed out that conservatives have faced threats from GOP leadership before for employing similar tactics. Meadows predicted that there could be similar blowback for centrists.

“When I voted against a rule they threatened to take away all travel, they threatened to take away any [National Republican Congressional Committee] contributions,” he told reporters earlier this week. “You know most of those people that were on the discharge petition are much closer to leadership than members of the Freedom Caucus — so I don’t see them voting against the rule.”

Under Boehner John Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE, it was not uncommon for members to be punished if they rebelled against leadership.

Meadows had his Oversight and Government Reform subcommittee gavel stripped, and then reinstated, after voting against leadership and failing to pay party dues.

And Rep. Daniel Webster Daniel Alan WebsterGaetz set to endorse primary opponent of fellow Florida GOP lawmaker Former cop Demings faces progressive pushback in veepstakes Overnight Energy: Biden campaign says he would revoke Keystone XL permit | EPA emails reveal talks between Trump officials, chemical group before 2017 settlement | Tensions emerge on Natural Resources panel over virtual meetings MORE (R-Fla.) and former Rep. Rich Nugent Richard (Rich) B. NugentRepublicans mull new punishments for dissident lawmakers Republicans fear retribution for joining immigration revolt Former aide will run to replace lawmaker MORE (R-Fla.) were both kicked off the House Rules Committee, also known as the Speaker’s committee, for voting against Boehner for Speaker in 2015.

Newhouse, who replaced one of them on the Rules panel, is sympathetic to the discharge petition effort. But Newhouse also said he would prefer to work through regular order, underscoring the sense that members of the Rules Committee are expected to remain in line with leadership.

"It’s the nuclear option, if there is no other alternative. It’s certainly not my first choice,” Newhouse said. “If we could work through regular order — I’m on the Rules Committee — [so] if we could work through regular order on this, that’s my preference.”

- Scott Wong and Mike Lillis contributed.