GOP support is building for an immigration bill authored by 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.) as House Republicans seek to avoid getting jammed by the White House and Senate.

The Goodlatte bill would call for more aggressive enforcement measures and would address thousands of young undocumented immigrants whose fate has been in limbo for months.

The stand-alone legislation, which Goodlatte plans to unveil Wednesday, is backed by 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’s leadership team.

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It has attracted support from both the moderate and conservative wings of the 239-member House Republican Conference, including 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 the Freedom Caucus’s Rep. Raúl Labrador (Idaho).

There are doubts, however, that it could clear the Senate, senior lawmakers said.

The White House and congressional leaders have been scrambling to figure out a solution for recipients of the Obama-era Deferred Action for Childhood Arrivals (DACA) program, which Trump is ending in March. Democrats are demanding protections from young immigrants enrolled in the program, but Republicans want to beef up border security and tackle other immigration issues in exchange for any DACA deal.

At a White House meeting with GOP and Democratic lawmakers on Tuesday, Trump appeared eager to strike a broader immigration deal. He proposed a two-step agreement where Congress would pass a major overhaul of the immigration system after dealing with the DACA recipients and securing the border.

“If you want to take it that further step, I’ll take the heat,” Trump told lawmakers. “You are not that far away from comprehensive immigration reform.”

In an interview, Freedom Caucus Chairman Mark Meadows Mark Randall MeadowsTrump reacts to Ginsburg's death: 'An amazing woman who led an amazing life' Trump carries on with rally, unaware of Ginsburg's death United Airlines, unions call for six-month extension of government aid MORE (R-N.C.) said Tuesday he’s “inclined” to back the Goodlatte bill based on what he’s heard so far.

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“I am very supportive of the work that Chairman Goodlatte has put forth in designing a bill to address the broader immigration issues we are facing,” said Meadows, who has not seen the final text yet. “I am inclined to support it based on the overview I have been briefed on.”

Goodlatte pitched his legislation during a GOP conference meeting Tuesday morning ahead of a bipartisan meeting at the White House aimed at hashing out a DACA solution.

The Judiciary chairman also took part in Tuesday’s White House meeting in which Trump and lawmakers agreed to limit future talks to four issues: shielding the young immigrant “Dreamers” from deportation, border security, chain migration and the visa lottery.

“Addressing these four issues — border security, the visa lottery, chain migration, and then something for DACA recipients — is a great first step,” Goodlatte told reporters as he returned to the Capitol. “I think there are a lot of other things that need to be done on immigration.”

While Goodlatte’s bill is expected to include those four categories, the chairman and others indicated that the House measure is expected to be more expansive by reflecting other conservative priorities. It is likely to include mandatory verification requirements for workers, known as E-Verify, according to CNN.

“That bill has some of those things, but has a lot more. That’s a lot bigger,” said Rep. Mario Diaz-Balart Mario Rafael Diaz-Balart'Trump show' convention sparks little interest on K Street Rep. Dan Meuser tests positive for COVID-19 Watchdog calls for probe into Gohmert 'disregarding public health guidance' on COVID-19 MORE (R-Fla.), who also attended the White House meeting.

Supporters of Goodlatte’s bill argue that it could garner 218 Republican votes in the House, which could help them avoid getting jammed with an unpopular immigration deal from the Senate.

“What we don’t want to take place is to get jammed by some Dreamer Act bill from the Senate, which some of us are concerned about,” said Rep. Mark Walker Bradley (Mark) Mark WalkerMike Johnson to run for vice chairman of House GOP conference The Hill's Morning Report - Sponsored by National Industries for the Blind - Woodward book revelations rock Washington The Hill's 12:30 Report — Presented by Facebook — Trump, Biden duel in final stretch | Vaccine trial on pause after recipient's 'potentially unexplained illness' | Biden visits Michigan | Trump campaign has 18 events in 11 states planned in the next week MORE (R-N.C.), chairman of the Republican Study Committee. “We hope that [Trump] supports what Goodlatte and people come up with.”

Trump did not take a position on Goodlatte’s proposal, though he called it a “good starting point” on Tuesday and insisted any legislation should be a “bill of love.”

But House GOP leadership has not yet committed to bringing the chairman’s bill to the floor.

“For whatever reason, there seems to be a little bit of internal debate over where that gets to the floor,” Walker said. “Leadership, they’re keeping their cards close to the vest.”

He added, however, that no one spoke out against the legislation during the conference meeting.

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Other Republicans were far more skeptical that a Goodlatte bill could garner 218 GOP votes in the House — or that such a measure could pass the Senate, where nine Democrats are needed to overcome a filibuster.

“Even if we did have 218 Republican votes for a DACA bill, it’s not going to be close to what the Senate passes. … We need to pass a DACA bill with over 300 votes,” said Rep. Charlie Dent Charles (Charlie) Wieder DentRepublican former Michigan governor says he's voting for Biden Biden picks up endorsements from nearly 100 Republicans Bush endorsing Biden? Don't hold your breath MORE (R-Pa.), co-chairman of the moderate Tuesday Group.

“We we can go through this exercise for a while, until we ultimately get jammed by the Senate. We’ll indulge all these folks with this fanciful notion that we’ll somehow pass a DACA bill with 218 Republican votes — and then unicorns fly.”