Washington (CNN) A rebellion by moderate House Republicans to force an immigration vote is widely expected to succeed this week, pushing members in at least one chamber of Congress to address one of the most hot-button topics in American politics months before the midterm elections and against the wishes of GOP leadership.

The final congressional signatures are likely to be added to a proposal in the next 36 hours that would bypass the wishes of House Speaker Paul Ryan and his deputies and ensure moderates a vote on immigration later this month.

But there's a catch.

Moderates say they will continue to negotiate with party leadership and conservatives -- even if they get enough support to force their own vote -- in hopes that a different, Republican-only immigration deal can spare the party leaders from an embarrassing and free-wheeling debate on the floor expected to benefit a bipartisan deal heavily supported by Democrats, while still delivering the immigration vote moderates need.

The House Republican infighting on this issue highlights how divisive immigration is to Republicans in Congress, particularly on questions of whether to support a pathway to citizenship for some undocumented immigrants as well as what to pair with it beyond a border wall, including substantial changes to the legal immigration system. The fight has also tested the power of leadership keeping moderates and conservatives at the negotiating table for weeks even while progress has seemed slow to nonexistent.

But as for staving off at least one key development, leadership's time appears to be up.

The fireworks are expected to begin Tuesday. That's the day members of the House return to Washington from the weekend and thus can physically sign a discharge petition, a rarely used and rarely successful House procedural maneuver that forces a vote on a bill (or in this case a series of bills) if half of House members sign on. It is also the last day the petition's organizers believe they have to get all the signatures if they want to hold the series of immigration votes before the end of the month.

The so-called petition has been steadily picking up signatures since it was introduced in early May, and stands just three members away from success . All but one Democrat has already signed, meaning at least two of those signatures will need to be more Republicans. The petition would ensure votes on four bills to address the Deferred Action for Childhood Arrivals program , which protected young undocumented immigrants who came to the US as children and President Donald Trump as ended, with the bills ranging from the most liberal to most conservative.

It is "extremely likely" those signatures will come on Tuesday, the leader of the effort, California Rep. Jeff Denham, told reporters Friday as he left one of the closed-door negotiations on immigration that party leadership has been convening to try to find another way to pass an immigration bill with only Republican votes.

And it's not just moderates who believe their effort will succeed Tuesday.

After a meeting last week in which lawmakers described progress but still substantial differences that would have to be resolved before a deal between conservatives and moderates could be reached, even conservatives were assuming the petition would move forward.

But rather than pledge to walk away, conservatives say they will view the approaching vote as a new shot clock for their efforts.

"Whether they can get 218 on Tuesday -- I fully anticipate that they will -- but that doesn't mean that we can't get a different deal and put it on the floor before June 25," said conservative Freedom Caucus Chairman Mark Meadows, a North Carolina Republican. "Part of me believes that they should have already done it, that way we can understand that we're going to continue to negotiate by all sides in good faith."

Inside difficult talks

Sources close to the negotiations described little progress over the weekend, though members had pledged on Friday they would work through the weekend if necessary.

Though talks continued, the sources said, they didn't resolve the major outstanding issues. And little if any actual legislative text has been produced.

The reality is that the conference is fighting against long-established divisions.

Moderates want to ensure that recipients of DACA have a clear path to become US citizens, but who would be eligible and how the path to citizenship would be structured is still under discussion.

Republicans are working through a proposal first conceived by Rep. Raul Labrador, a conservative from Idaho, which would create a new type of visa based on a point system and would apply to a larger group of immigrants like DACA recipients though not limited to them -- a way to address conservatives' diametric opposition to what they call a "special pathway" to citizenship they say rewards people who live in the US illegally. The visas would likely come from other existing categories, so as not to add to the number of legal immigrants admitted to the US annually, and there are likely to be some cuts to family-based migration and the diversity visa, as Trump has sought.

Meadows said "there is a growing consensus" around the citizenship issue, but "there's still some details that need to be worked out on that option."

But even as lawmakers described getting much closer on what has been the thorniest issue thus far, the citizenship question, addressing the next issue of border security has proven more difficult than expected, they said. Meadows expressed surprise at how sticky that had become. While sources and lawmakers say giving the President money for his marquee campaign promise of a physical wall in some capacity seemed generally acceptable. a host of changes to the law on the immigration enforcement side sought by conservatives are much less settled.

"We still have to deal with a lot of big, controversial issues," said Rep. Mario Diaz-Balart, a moderate Republican from Florida, said Friday before members left for the weekend.

"I'm disappointed that more issues continue to get added when we're trying to close out," Denham said.

Rather than being new issues, other members described them as issues that were always there, members just hadn't been able to talk about them yet.

"You bring things up now and some people say, 'Well, that's new I never heard it before.' It wasn't new to me, we just never got to it," said conservative Freedom Caucus member Scott Perry, a Pennsylvania Republican. "For me we're vetting more of the ideas that need to be vetted, but for some people I think they feel like we're getting further away because they didn't hear about those things before."