Republican leaders are facing long odds as they scramble to thwart an internal rebellion over immigration just months before November’s midterm elections.

The leaders are attempting to broker a deal that satisfies competing factions of their restive conference and defuses a push by mutinous centrists threatening to force action to protect undocumented immigrants in a series of head-to-head floor votes that would highlight deep GOP divisions over an issue that has long been radioactive within the party.

The dispute has centered largely on what legal protections should be extended to those living in the country illegally, and to whom they should apply — thorny enough questions on their own. But the leaders’ effort was further complicated on Thursday, when President Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE warned that he'd veto any bill to shore up the Deferred Action for Childhood Arrivals (DACA) program if it fails to fund his favored wall at the U.S.-Mexico border.

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“Unless it improves a wall — and I mean a wall, a real wall — and unless it improves very strong border security, there’ll be no approvals from me, because I have to either approve it or not,” Trump said in an interview with Fox News Channel.

The president’s demand is just the latest headache for 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.) and his leadership team, who are in delicate negotiations to appease both the reform-minded centrists — whose discharge petition is inching closer to the 218 signatures it needs to force a vote — and conservative immigration hard-liners vowing to oppose any proposal that would, in their eyes, provide “amnesty” to immigrants in the country illegally.

Ryan, in reluctantly taking the Speaker’s gavel in 2015, had promised members of the far-right Freedom Caucus that he wouldn’t consider any immigration bill that lacks the backing of a majority of Republicans — a vow those conservatives haven’t forgotten almost 30 months later. And the Speaker’s lame-duck status — he’s retiring at the end of the year — has only weakened his hand as he tries to exert control over his troops and avoid an all-out immigration fight heading into elections where the issue is sure to play a prominent role.

“What we're trying to do is find where the consensus sweet spot is,” Ryan told reporters in the Capitol last week. “Immigration is an issue that has a lot of passionate positions.”

Hovering over the debate through the Memorial Day recess is the centrists’ claim that their discharge petition — a rarely used procedural step to force votes to the floor against the wishes of majority party leaders — already has enough Republican support to hit the 218 mark if Ryan fails to orchestrate a deal quickly when Congress returns to Washington early next month.

“They are at the point where they are confident I've got more than 218 votes,” said Rep. Jeff Denham Jeffrey (Jeff) John DenhamBottom line Bottom line Lobbying world MORE (R-Calif.), one of the leading forces behind the discharge petition. “They want to get [a deal] done.”

The window for reaching such an agreement, though, is closing quickly. Republicans will huddle in the Capitol on June 7 for a two-hour meeting designed to reach a consensus. If none emerges, then more Republicans are expected to endorse the discharge petition, forcing votes on several immigration bills as early as June 25.

“I believe the drop-dead date is June 7,” said 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 deputy whip, who has not endorsed the petition but remains open to doing so. “We’re giving them 10 days to see what happens.”

Ryan, last year, had promised the Freedom Caucus a vote on their preferred immigration bill, a conservative proposal championed by Judiciary Committee Chairman Bob Goodlatte Robert (Bob) William GoodlatteNo documents? Hoping for legalization? Be wary of Joe Biden Press: Trump's final presidential pardon: himself USCIS chief Cuccinelli blames Paul Ryan for immigration inaction MORE (R-Va.), and they’re frustrated with the Speaker’s inaction since then. In its current form, the proposal lacks the backing to pass the House, but conservatives want an opportunity to show their support nonetheless.

“There are some of us who, even with the Goodlatte bill, believe that a slight amendment here or there may get us to 218,” Rep. 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.), chairman of the Freedom Caucus.

“We’re tired of talking about it. We think it’s time to vote,” he said.

If the discharge petition were to succeed, it would prompt a “Queen of the Hill” process featuring votes on four separate proposals: the conservative Goodlatte bill; the liberal Dream Act; a bipartisan proposal, sponsored by Reps. Will Hurd William Ballard HurdHillicon Valley: Oracle confirms deal with TikTok to be 'trusted technology provider' | QAnon spreads across globe, shadowing COVID-19 | VA hit by data breach impacting 46,000 veterans House approves bill to secure internet-connected federal devices against cyber threats House Democrats' campaign arm reserves .6M in ads in competitive districts MORE (R-Texas) and Pete Aguilar Peter (Pete) Ray AguilarRep. Robin Kelly enters race for Democratic caucus vice chair Pelosi seeks to put pressure on GOP in COVID-19 relief battle Races heat up for House leadership posts MORE (D-Calif.), combining DACA protections with new efforts to strengthen border security — but without explicit funding for Trump’s wall; and a yet-unknown bill of Ryan’s choosing. The proposal that wins the most votes, beyond 218, would go to the Senate.

The agreement GOP leaders are seeking instead would feature votes on only two immigration proposals: Goodlatte’s legislation, perhaps with amendments, and a bill providing permanent legal status — and an eventual path to citizenship — for the so-called Dreamers. Such a deal would preclude an embarrassing “Queen of the Hill” scenario, which Republican leaders in Congress and the White House contend lends too much power to the minority Democrats.

“That would be like turning over the House to Nancy Pelosi Nancy PelosiPelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare House lawmakers reach deal to avert shutdown Centrist Democrats 'strongly considering' discharge petition on GOP PPP bill MORE,” Marc Short, Trump’s legislative director, said Friday, referring to the Democratic leader.

Leadership allies say they’re confident Ryan can bridge the divide and keep the more liberal bills off the floor.

“They want to continue having Republicans lead on that issue [and] the president wants to lead on that issue,” said GOP Rep. Tim Walberg Timothy (Tim) Lee WalbergThe health care crisis no one is talking about Overnight Defense: Pentagon policy chief resigns at Trump's request | Trump wishes official 'well in his future endeavors' | Armed Services chair warns against Africa drawdown after trip GOP chairman after Africa trip: US military drawdown would have 'real and lasting negative consequences' MORE, who has dozens of farms in his southern Michigan district. “So I’m hoping that ultimately our caucus will come together and put an immigration bill across the line.”

Rep. Carlos Curbelo Carlos Luis CurbeloGOP wants more vision, policy from Trump at convention Mucarsel-Powell, Giménez to battle for Florida swing district The Memo: GOP cringes at new Trump race controversy MORE (R-Fla.), the sponsor of the discharge petition, said “a major discussion area” remains the question of citizenship. The centrist DACA supporters are fighting to ensure those immigrants “have a bridge into the legal immigration system,” he said, while conservatives are adamant that they don’t receive a “special” path, akin to jumping in line. But the nuances surrounding that distinction have yet to be worked out.

“You have to define ‘special,’ ” Curbelo said, declining an attempt to do so.

Another wild card in the debate is the question of how many Democrats will endorse the discharge petition. While 190 Democrats have already signed on, three lawmakers representing districts on the Texas-Mexico border — Reps. Filemon Vela Filemon Bartolome VelaHispanic Caucus asks for Department of Labor meeting on COVID in meatpacking plants The Hill's Campaign Report: Biden builds big lead in battleground Florida Texas Democrat proposes COVID-19 victims' compensation fund MORE, Henry Cuellar and Vicente González — have refused to do so, citing fears that the process would facilitate new border wall construction at the expense of their communities.

Trump’s veto threat over wall funding will only heighten those concerns, while raising new doubts that there’s an agreement to be had that can win the support of most House Republicans, Senate Democrats and the president.

Indeed, Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellPelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Senate GOP aims to confirm Trump court pick by Oct. 29: report Trump argues full Supreme Court needed to settle potential election disputes MORE (R-Ky.) has warned that he won’t consider any immigration bills that Trump won’t sign.

“We have to make law,” McConnell told The Wall Street Journal on Thursday, “not just spin our wheels.”

Scott Wong contributed.