Updated at 3:20 p.m. with new developments.

WASHINGTON — Thirty-four House Republicans, including two Texans, are calling for Congress to pass a permanent fix to the Deferred Action for Childhood Arrivals program by year’s end —adding a new wrinkle to a looming fight over the immigration program and a potential government shutdown.

On Tuesday, the group of Republicans — including Ennis Rep. Joe Barton and San Antonio Rep. Will Hurd — wrote to Speaker Paul Ryan to say that while they agree with President Donald Trump that the Obama-era program should not have been enacted through executive order, Congress should act this month to protect from deportation immigrant children who were brought to the country illegally.

“We are compelled to act immediately because many DACA recipients are about to lose or have already lost their permits in the wake of the program’s rescission. Not acting is creating understandable uncertainty and anxiety amongst immigrant communities,” the lawmakers wrote.

The news comes a day after Texas Sen. John Cornyn flatly ruled out a demand by some Democrats to include a legislative fix for DACA in talks over an upcoming must-pass spending bill this month — instead of taking up the issue, along with border security measures, separately.

Cornyn, the No. 2 Republican leader, has accused Democrats of a “hysterical and cynical ploy” by insisting that a plan to protect the estimated 800,000 young immigrants, including 124,000 in Texas, from deportation be reached by year’s end — lest Democrats vote against a spending bill needed to avert a government shutdown.

On Tuesday, Cornyn said Republicans are willing to enter into "good faith investigations" over DACA "but they do not belong in an end-of-the-year spending appropriations debate."

Stopgap spending measure

The government’s spending — now funded by a stopgap measure approved in September — is set to expire Dec. 8. But a gridlocked Congress is still unprepared to pass traditional appropriations bills, and is now eyeing a potential two-week stopgap measure, with talk of another short-term spending bill to fund the government through January.

Illinois Sen. Dick Durbin, the No. 2 Democrat in his chamber, has said he’ll push others in his party to vote against a stopgap measure this month if a DACA solution isn't reached soon.

Along with Sen. Lindsey Graham, R-S.C., he's a co-sponsor of the bipartisan "Dream Act" that would grant permanent legal status to hundreds of thousands of young people who arrived in the country before age 18, and who passed security checks and met other criteria.

Durbin is leading the charge of Democrats suggesting they'll leverage a potential shutdown in order to seal a deal for so-called Dreamers, who face the risk of deportation after Trump moved to phase out the Obama-era program in early September. The president extended deportation protections through March.

"There's too much at stake here. We can't let this slip into January, February with a March 5 deadline," Durbin toldThe Washington Post last week. "It should be done, it can be done, easily, simply and quickly."

Cornyn proposal

On Tuesday, Senate Judiciary Chairman Chuck Grassley, Cornyn and a handful of Republican senators announced the “SECURE Act” that would boost border security measures and reauthorize the E-Verify program.

It also includes a proposal by Graham, backed by Durbin and others, that would effectively grant current DACA recipients protection from deportation for three years.

Durbin, who wants permanent protections for Dreamers, dismissed the proposal, saying it's "not a good-faith effort."

The Cornyn-Grassley immigration proposal is not a good faith effort to protect #Dreamers. My statement → pic.twitter.com/zfv6ohCYAn — Senator Dick Durbin (@SenatorDurbin) December 5, 2017

“The laundry list of unrelated immigration bills which they have offered is designed to delay and stop any serious bipartisan effort to solve this crisis created by the Trump Administration on Sept. 8,” he said on Twitter, pledging to continue efforts to pass the Dream Act.

The Grassley-Cornyn measure was also slammed by Julieta Garibay, Texas director of the pro-DACA group United We Dream.

"We want to be perfectly clear that we are calling for a clean Dream Act before Congress goes home for Christmas," she said in a statement. "We will not accept Senator Cornyn's, or any other extremist members of Congress', attempts to make us second-class citizens, or their efforts to terrorize and deport our families in exchange for protections for immigrant youth."

Still, Senate Minority Leader Chuck Schumer tamped down talk of a shutdown over DACA on Tuesday.

He, along with Ryan, House Minority Leader Nancy Pelosi and Senate Majority Leader Mitch McConnell are expected to meet with Trump at the White House this week to discuss a stopgap spending measure. Talks over DACA and border security are "moving in the right direction," he told reporters.

Senate Min Leader Chuck Schumer dismisses idea that there will be a govt shutdown over deportation protections for #Dreamers. Bipartisan talks for a year-end deal on #DACA and border security are going well, he says. ``We think we're moving in the right direction there.'' — Laura Litvan (@LauraLitvan) December 5, 2017

House support

The GOP members who wrote to Ryan on Tuesday include several moderate Republicans, though Barton is a member of the conservative House Freedom Caucus. The longtime Texas leader recently announced plans to retire following this term after embarrassing images from a previous extramarital relationship were made public.

A number of Texas Republicans have said they favor allowing the Dreamers to remain in the country, but Barton is the sole Texas House Republican to sign on to the latest Dream Act, a bipartisan bill that would protect Dreamers from deportation.

He's also a co-sponsor of a Republican-led bill introduced by Florida Rep. Carlos Curbelo that, similar to the Dream Act, would grant Dreamers legal protections and a path to citizenship.

Curbelo, who has threatened to vote against a year-end spending measure if it doesn't include a DACA fix, also co-signed the letter to Ryan on Tuesday.

“They’ve been educated here, they’ve grown up here, and in most cases they don’t have family in their country of origin to go back to, so why not take advantage of the investment we’ve made in them and help them become productive adults here in the United States?” Barton said in September.

Hurd, who represents a key swing district in West Texas, is one of three Texans Ryan tapped in September for an informal working group on the DACA predicament. He has not, however, signed on to the Dream Act or Curbelo's measure.

The letter to Ryan doesn't endorse a specific piece of legislation, nor does it include threats to shut down the government if a vote on DACA protections isn't held this month.

Frank Sharry, executive director of America's Voice Education Fund, which advocates for immigrants' rights, was among those applauding the Republicans' move. In a statement Tuesday, he noted that it would take just 24 Republicans to join House Democrats to pass a DACA-related measure this month.

"With today's letter, it's clear that the votes are there to resolve Dreamers' crisis before the end of the year," he wrote. "... Dreamers need relief urgently and now, not some vague promise about standalone legislation at some point down the road."