Updated

House Speaker Paul Ryan was scrambling Thursday to settle a brewing insurrection among Republican lawmakers over immigration as moderates in coalition with Democrats look to force a debate on a series of immigration bills.

Ryan held a lengthy meeting with the House GOP conference Thursday morning in an effort to dissuade proponents of a “discharge petition” from forcing the House into a series of fiery floor debates in the coming weeks.

He emerged from the session optimistic but with no agreement secured. He said that leadership was working on compromise legislation that would meet President Trump's four pillars for immigration reform that he would sign -- which include tighter border security and immigration restrictions.

"We are reaching consensus on how to address those four pillars," he said, before adding that "a discharge position will result in no law."

One of the House moderates, Rep. Jeff Denham, R-Calif., said that his group tentatively agreed to an offer from conservatives, but that his group will need to see the specifics in writing first.

Members also met for several hours Wednesday with House leaders as part of the move to stave off the discharge petition and come to an agreement on an immigration deal.

WHAT HAPPENS IF DISCHARGE PETITION SECURES 218 SIGNATURES 

A discharge petition is a rarely successful gambit to force consideration of a bill that requires the signatures of 218 members.

But the group of centrists -- headed up by Florida Rep. Carlos Curbelo and including other moderates like Denham -- is eager to compel action on immigration. They are reportedly two votes away from securing the 218 votes.

The lawmakers want to push a fix for the Obama-era Deferred Action for Childhood Arrivals (DACA), which granted protection to some illegal immigrants who came to the country as children.

Trump announced the program’s expiration last year, though its termination has been stalled by court orders. He has called on lawmakers, though, to “legalize DACA” as part of a broader immigration bill that would tighten border security and immigration laws -- including a wall on the southern border.

That has not yet happened.

But how to enshrine DACA protections into law is a nettlesome issue. While some moderates envision a path to citizenship for DACA recipients, conservatives -- particularly those in the House Freedom Caucus -- have called such a move tantamount to amnesty.

"We've got the rule of law in this country, and nobody gets special consideration," said Rep. Scott Perry, R-Pa.

But some conservatives are prepared to provide such a pathway if the legislation includes up to $25 billion of funding for the wall, the end to the diversity lottery visa and the end of so-called “chain migration” -- limiting the number of relatives whom immigrants can sponsor for visas.

Rep. Mark Walker, R-N.C., who has proposed such legislation, has said the tighter curbs on family-based migration they demand would depend on how many immigrants would be eligible for the citizenship pathway.

"This is a difficult issue," Ryan told reporters Thursday. "We're trying to figure out what the sweet spot is."

But should members not come to a deal, Fox News is told that members prepared to sign a discharge petition would move forward soon.

The petition would force House votes on four immigration/DACA bills, ranging from liberal to hardline. One more conservative bill is from House Judiciary Committee Chairman Bob Goodlatte, R-Va. Another would be the House Democrats’ DREAM Act. 

There would also be whatever bill Ryan puts forward, as well as a bill by Reps. Jeff Denham, R-Calif., Will Hurd, R-Texas and Pete Aguilar, D-Calif. That measure bolsters border security and grants legal status to many DACA recipients.

Whichever bill obtains the most votes (not necessarily 218) would advance to the next round, followed by a vote to pass or reject the bill.

GOP leaders and conservatives are concerned that the discharge petition would produce a liberal bill, with Democrats joining Republicans to push it through. Such a bill would likely be killed off in the Senate or by the White House, but GOP leaders fear it could alienate conservatives ahead of the November midterms. 

In February, a series of four plans dealing with immigration fell by the wayside in the Senate, with no amendment crossing the 60 votes needed to pass that chamber. 

Because of the multitude of restrictions on discharge petitions, there have only been two successful petition efforts in the last 16 years. One was on a campaign finance reform bill in 2002. The other was to reauthorize the Export-Import Bank in 2015. House leaders rarely lose control of the floor via a discharge petition campaign.

Discharge petition supporters face a deadline of June 11 to collect the necessary signatures, as the House can only consider discharge petitions on the second and fourth Mondays of each month. Lawmakers could sign the petition early next week if Ryan's plan isn’t to their liking.

Fox News’ Chad Pergram, Alex Pappas and The Associated Press contributed to this report.