House 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.) on Thursday tamped down a Republican insurrection on immigration — at least temporarily — with vows to “put pen to paper” on a compromise bill to protect the young undocumented immigrants known as Dreamers.

During a two-hour, closed-door meeting in the basement of the Capitol, Ryan and other GOP leaders urged their troops not to endorse a procedural move to force votes on the Deferred Action for Childhood Arrivals (DACA) program — known as a discharge petition — and instead give leaders more time to forge a compromise that can win 218 Republican votes.

“The next step is to start putting pen to paper and get legislation to the floor,” the Wisconsin Republican told reporters afterwards.

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The promise seems to have bought them some time in their search for an elusive DACA deal that can win the support of centrist immigration reformers and conservative hardliners. Indeed, several moderates who have remained open to signing the petition said after the meeting that they’ll refrain from doing so while GOP leaders seek a compromise.

“We've still got time, there’s a general outline and they’re putting pen to paper,” said 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.), who said he’s waiting to see the details of the bill before making a decision about the petition.

“Today's not the deadline.”

Still, the window for reaching a deal may be short.

By the obscure rules of the discharge petition, the supporters hoping to ensure DACA votes this month have until June 12 to gather the 218 signatures needed to force the issue to the floor. And while Ryan indicated there’s no official deadline — “Our new deadline is not to have a deadline,” he said — McCarthy seems to be eying next week as a more concrete target.

“That comes down to the 12th, so we're moving towards getting a bill,” McCarthy told The Hill.

That leaves leadership with just five days to craft legislation they believe can garner 218 GOP votes. Supporters of the petition are two Republican signatures away from the number of members needed to bypass leadership and bring the “Queen of the Hill” rule to the floor.

“We are looking forward to seeing an agreement put on paper,” Rep. Jeff Denham Jeffrey (Jeff) John DenhamBottom line Bottom line Lobbying world MORE (R-Calif.), one of the leading forces behind the discharge petition, told reporters following the meeting. “We finished a very productive meeting. We've had a lot of productive meetings, but ultimately this is about writing a bill that makes sense for the country.”

Ryan and other GOP leaders, who have been scrambling to forge a DACA compromise that would make the discharge petition unnecessary, had hoped to have such an agreement finalized to present to the conference at Thursday’s gathering. Indeed, that was the expectation of some of the Republicans going in.

“I thought that myself,” said Rep. Walter Jones Walter Beaman JonesExperts warn Georgia's new electronic voting machines vulnerable to potential intrusions, malfunctions Georgia restores 22,000 voter registrations after purge Stacey Abrams group files emergency motion to stop Georgia voting roll purge MORE (R-N.C.).

But the talks between leaders, centrists and conservatives seeking such an agreement have failed to bear fruit.

There was “a lot of good discussion,” said, Rep. Mark Meadows Mark Randall MeadowsThe Hill's Morning Report - Sponsored by Facebook - GOP closes ranks to fill SCOTUS vacancy by November House moves toward spending vote after bipartisan talks House Democrats mull delay on spending bill vote MORE (R-N.C.), chairman of the Freedom Caucus, “and yet at the same time, there is no consensus.”

Still, Ryan set up a format that avoided confrontation on an issue that's divided the conference for years.

“The Speaker set exactly the right tone and that is, ‘We're all Republicans, we are now in the majority and thus we have to demonstrate that we can cooperate in order to do something good,’” said Rep. Dana Rohrabacher Dana Tyrone RohrabacherDemocrat Harley Rouda advances in California House primary Lawyers to seek asylum for Assange in France: report Rohrabacher tells Yahoo he discussed pardon with Assange for proof Russia didn't hack DNC email MORE (R-Calif.). “I think he struck a tone that all of us felt good about and there's some open-minded discussion going on right now.”

In a sense, the Republicans — despite almost six years hammering the DACA program and nine months vowing to move legislation to salvage it — are back at square one.

“I still don’t think they have a pathway to get there, and now they’re going to put pen to paper and we’ll see what it looks like,” said Rep. Roger Williams John (Roger) Roger WilliamsThe Hill's 12:30 Report - Presented by Facebook - Yoho apologizes for accosting AOC Ocasio-Cortez accosted by GOP lawmaker over remarks: 'That kind of confrontation hasn't ever happened to me' Cook shifts 20 House districts toward Democrats MORE (R-Texas).

“I think it’s the beginning of the process.”

In seeking an immigration compromise, GOP leaders are leaning heavily on a four-tiered outline offered by President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE earlier in the year. That package combines DACA protections with three other features: tougher security, including a border wall; a reduction in family migration; and an end to the diversity visa lottery, which promotes the arrival of people from low-immigration countries around the globe.

The most significant sticking point remains the ongoing disagreement between centrists and conservatives over how — or even whether — Dreamers can attain citizenship rights.

Lawmakers on all sides of the debate said the meeting was cordial. Rep. Leonard Lance Leonard LanceThomas Kean wins GOP primary to take on Rep. Tom Malinowski Gun debate to shape 2020 races GOP fears Trump backlash in suburbs MORE (R-N.J.), who’s signed the discharge petition, said it was the most civil conference gathering he’s attended since arriving in Washington. But it was, by all accounts, also something of a free-for-all, with lawmakers promoting their preferences — and airing their grievances — on issues as diverse as guest workers, and e-verify.

Rohrabacher, for instance, offered a proposal to offer visas to 50,000 immigrants per year — for a $1 million fee.

Many of those proposals are non-starters in the current DACA debate, however, and many of the moderate Republicans are growing impatient with their leadership’s inaction, both in staging votes and offering an alternative proposal for propping up DACA.

“The Speaker obviously doesn’t like the discharge petition. That’s fine, bring something to the floor,” said 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’s endorsed the petition.

“The buffet’s full. Either starve to death or go get something to eat.”

While many members appeared optimistic they could reach a deal that satisfies all factions of the conference, they also noted the pressure on leadership created by the discharge petition remains a factor in the debate.

“Clearly it [the discharge petition] has accomplished a great deal and this never would have occurred without the threat of it,” Rep. Tom Reed Thomas (Tom) W. ReedCentrist House group offers bipartisan COVID-19 relief deal House approves two child care bills aimed at pandemic Diabetes Caucus co-chairs say telehealth expansion to continue beyond pandemic MORE (R-N.Y.), a petition signer, told the Hill.

“So the threat’s not going to leave,” he added, “so let's see if there's a way to resolve it without that. And if not, then this is going to come to a head.”

Still, most Republicans walked out of the meeting without a clear idea of what lies ahead.

“It's just a mystery, still, whether we’ll be able to get the signatures or whether they'll bring some proposals to the floor,” said Rep. Ileana Ros Lehtinen (R-Fla.), another petition signer. “Some of us are really frustrated to not be able to have a vote.”

Scott Wong contributed.