A group of House Republicans unveiled their own solution to an Obama-era immigration program on Wednesday as questions persist over how congressional leadership and the White House will work out a deal on the issue.

The bill, backed by the chairmen of the House Judiciary and Homeland Security committees, would call for more aggressive enforcement measures in exchange for addressing the thousands of young undocumented immigrants whose fate has been in limbo for months.

Backers of the bill are hoping to rally GOP support in the coming days, seizing on the concerns of their House colleagues that they could find themselves stuck with a more narrow immigration deal from the Senate that doesn’t address as many conservative priorities as their own plan.

“Our focus will be on showing that there is very strong support in the House for this approach,” House 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.) said at a press conference Wednesday.

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But even the Goodlatte bill has run into some resistance within the GOP, underscoring the challenge for Republican leadership in protecting thousands of young undocumented immigrants in a way that pleases their own ranks.

Congress has been racing to come up with a permanent legal solution for recipients of the Deferred Action for Childhood Arrivals (DACA) program, which Trump announced he would end come March. The program grants work permits to undocumented immigrants who were brought to the U.S. as children.

Complicating negotiations further was a decision by a federal court in San Francisco on Tuesday evening that temporarily blocked the Trump administration from rolling back the program.

Trump met with congressional leaders earlier Tuesday to hash out a potential deal at the White House, where negotiators agreed to limit future talks to four issues: shielding so-called Dreamers from deportation, increasing border security, changing the weighting for family relationships when granting legal status and reforming the visa lottery.

Still, there is a growing contingent of House conservatives who would rather push ahead with their own plan, which has attracted support from both the moderate and conservative wings of the 239-member House Republican Conference.

Centrist Rep. Martha McSally Martha Elizabeth McSallySenate Republicans face tough decision on replacing Ginsburg Democratic senator calls for eliminating filibuster, expanding Supreme Court if GOP fills vacancy What Senate Republicans have said about election-year Supreme Court vacancies MORE (Ariz.) and Rep. Raúl Labrador (Idaho), a member of the conservative Freedom Caucus, are chief co-sponsors of the bill.

“It’s better for us to do a bill in the House that is consistent with what the American people elected us to do,” Rep. Jim Jordan James (Jim) Daniel JordanHouse passes resolution condemning anti-Asian discrimination relating to coronavirus Republicans call for Judiciary hearing into unrest in cities run by Democrats Trump, GOP seek to rebut Democratic narrative on night one MORE (R-Ohio), a member of the Freedom Caucus, told The Hill.

Goodlatte’s measure would provide DACA recipients with a temporary, three-year legal status that could be renewed indefinitely, but immigrants would not be offered a path to citizenship.

The measure would authorize $30 billion to build a border wall and invest in other border security measures, end chain migration and end the diversity visa lottery program — all of which were pillars outlined at Tuesday’s White House immigration meeting.

But the Goodlatte bill would go a few steps further by mandating E-Verify, a system that crosschecks every new employment contract with a federal immigration status database; allowing the Justice Department to withhold grants from so-called sanctuary cities; and increasing the criminal penalties for deported criminals who return to the U.S. illegally.

Under the proposal, immigration levels would be reduced by 25 percent overall, according to a summary sheet.

Goodlatte and Homeland Security Committee Chairman Michael McCaul Michael Thomas McCaulEngel subpoenas US global media chief Michael Pack Russia continues Navalny probe, wants to send additional investigators to Germany Pompeo says 'substantial chance' Navalny poisoning was ordered by senior Russian official MORE (R-Texas) pitched their immigration plan to the Republican Study Committee on Wednesday, a day after making the case to leadership that the measure should receive a floor vote — something leaders have not yet committed to do.

“It’s kind of a bellwether to see how many co-sponsors we get on the bill,” McCaul told The Hill.

Goodlatte’s bill also appeared to have the support of outside groups that advocate for reduced immigration. Roy Beck, president of NumbersUSA, said the Goodlatte plan "is looking very, very good."

Beck said NumbersUSA's top two priorities are to end chain migration and mandate E-Verify.

"The one big issue I have with the president is that he’s not talking about mandatory E-Verify in the first round," said Beck. "Our feeling is if you do an amnesty, you’ve gotta stop the reason why you’re doing more amnesties, you’ve got to stop the reason why employers are hiring illegal foreign workers."

Beck added that the Goodlatte bill is a compromise on "a complex issue."

"It’s not the compromise that Dick Durbin Richard (Dick) Joseph DurbinMcConnell focuses on confirming judicial nominees with COVID-19 talks stalled Senate Republicans signal openness to working with Biden Top GOP senator calls for Biden to release list of possible Supreme Court picks MORE would want, but it involves quite a few compromises from our standpoint," he said.

Trump did not take a position on Goodlatte’s proposal, though he called it a “good starting point” on Tuesday.

“We have the sense that the White House is backing this effort. And I think that was exemplified in yesterday’s meeting, when he said the Goodlatte-McCaul bill is going to be the starting ground for these negotiations,” McCaul said at Wednesday’s press conference. “Now, where this ends up? I don’t have a crystal ball.”

House Majority Leader Kevin McCarthy Kevin Owen McCarthyTrump asked Chamber of Commerce to reconsider Democratic endorsements: report The Hill's Morning Report - Sponsored by The Air Line Pilots Association - White House moves closer to Pelosi on virus relief bill Trump's sharp words put CDC director on hot seat MORE (R-Calif.) also told reporters Wednesday evening that he thought Goodlatte's DACA effort was a "good start."

"The Goodlatte bill's a good bill," McCarthy said.

But leadership, which is still scrambling to strike a DACA deal with Democrats, has not yet promised to put the measure on the House floor amid doubts about whether it can get 218 GOP votes.

Members who represent the agricultural industry were pleased that the GOP bill creates an agricultural guest worker program, but they balked that the proposal would also require E-Verify for new workers.

Bill sponsors say it’s a necessary tradeoff in exchange for allowing more agricultural visas, because they want to ensure that employers only hire legal workers.

“Some people are for it, some people are against it. But if we’re going to have an agricultural visa, there should be an E-Verify program,” Labrador told The Hill. “In order for the agricultural members to get the visas that they want, they need to understand that we also need an E-Verify program."

The plan does face some Republican opposition, with moderates like 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.) wanting a DACA deal to include a pathway to citizenship while immigration hard-liners like Rep. Steve King Steven (Steve) Arnold KingGOP leader: 'There is no place for QAnon in the Republican Party' Loomer win creates bigger problem for House GOP Win by QAnon believer creates new headaches for House GOP MORE (R-Iowa) say they are unlikely to support the Goodlatte bill because it provides legal status to thousands of immigrants who are in the country illegally.

“This bill, I don’t even have to look at it to know that this has DACA amnesty. ... That’s sacrificing the rule of law,” King told The Hill. “I’m worried that my own leadership is going to jam us with something unpopular."

"I’m worried about jams coming in any direction," he added.

– Rafael Bernal contributed

Updated: 6:53 p.m.