The meeting did, however, buy Republican leaders more time to come up with answers.
But lawmakers emerged without a deal. Another member of that group, Rep. Dave Brat, R-Va., said the idea has been discussed but cautioned that there are "tons of moving pieces to it". Ryan is retiring after this term.
The progress came after House GOP members spent two hours behind closed doors huddling Thursday morning, a rare full-party confab on the issue of immigration. But some centrist Republicans did, as they continued to press - against Ryan's will - a rare procedure to force House votes on immigration legislation, including a bill mainly supported by Democrats. But moderates like Curbelo have grown increasingly frustrated with the legislative stalemate, prompting them to start the discharge petition.
The meeting was "intensive and argumentative - the way it should be", Mast said. He vowed that by Tuesday it was "extremely likely" they would have the signatures needed to push the roll calls. A day earlier, some said they expected House Speaker Paul Ryan to suggest ideas for ending the standoff between moderates who want a pathway to citizenship for "Dreamers" brought into the US illegally as children, and conservatives opposed to that idea. It would be unlikely to get substantial Democratic support, given widespread opposition to numerous measures Trump has said are necessary for his signature.
Republican leaders began convening the talks between moderate and conservative Republicans when dueling uprisings collided.
Painfully aware of those divisions, leaders had seemed happy to sidestep the issue as they head into campaign season for the fall midterm elections until the moderates' rebellion forced their hand.
Another is the unpopularity of House Democratic Leader Nancy Pelosi. Ryan said he was giving lawmakers space to find a solution.More news: Dennis Rodman Tears Up While Discussing Trump's Meeting with Kim Jong
More news: Ariana Grande Tweets About Her Happiness After Engagement Reveal!
More news: Trump Kim summit: United States president hails deal after historic summit
Some optimistic congressmen said they were going to work on a Republican-driven compromise measure that could make its way through the House by July.
Fractured House Republicans huddled privately Thursday as leaders tried pushing them toward consensus on immigration, racing the clock and trying to defuse a civil war within the party that threatens their effort to keep control of the chamber in November's elections. Rep. Carlos Curbelo, R-Florida, another one of the moderate leaders, said the goal would be to not lower overall legal immigration levels but shift some total visas into employment categories rather than family-based categories. Conservatives have been agitating for months for a vote on hard-line immigration legislation authored by House Judiciary Chairman Bob Goodlatte, R-Va.
The premise of the Villaraigosa campaign was to tack toward the center of California's political spectrum, embracing targeted government assistance and a liberal immigration policy, while pumping the brakes on expensive programs like a proposed single-payer health care system, enthusiastically supporting charter schools and occasionally wading into conservative rhetorical territory about red tape and bureaucratic excess.
There's uncertainty over what would happen after the end of the eight-year visa program, but Denham said participants have characterized the proposal as a bridge to the legal immigration system - which suggests a pathway to remaining in the US permanently.
Trump ended protections for the DREAMers a year ago by unwinding an Obama-era program, called Deferred Action for Childhood Arrivals (DACA), which grants legal status and work permits for approximately 700,000 DREAMers.
The major hang-up in GOP talks has been how, as the moderates have demanded, to offer a chance for citizenship to young "Dreamer" immigrants.
Conservatives have been adamant about not providing a "special" process carving out a unique way for Dreamers to gain legal status, and some of them bristled at Denham's narrower description. In addition to funding for a wall along the border with Mexico, conservatives are pressing for changes making it harder to pursue an asylum claim, used by people who fear persecution in their home countries, and punishments for so-called sanctuary cities, which don't fully assist federal authorities seeking to remove illegal immigrants. Conservatives also want to strengthen immigration enforcement inside the country.