WHITE SULPHER SPRINGS, W.Va. — Senate Republican Conference Chairman John Thune John Randolph ThuneThe Hill's 12:30 Report - Presented by Facebook - Don't expect a government check anytime soon The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Trump contradicts CDC director on vaccine, masks Senate GOP eyes early exit MORE (S.D.) says that congressional negotiators may settle on a slimmed-down immigration deal that leaves aside some of President Trump Donald John TrumpHR McMaster says president's policy to withdraw troops from Afghanistan is 'unwise' Cast of 'Parks and Rec' reunite for virtual town hall to address Wisconsin voters Biden says Trump should step down over coronavirus response MORE’s priorities.

Thune said Congress may wind up passing a bill to protect illegal immigrants known as Dreamers from deportation in exchange for more money for border security.

Under this scenario, Trump’s demand that Congress limit immigration preferences for nonnuclear family members and end the diversity visa lottery program would be set aside for a later debate.

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“If we can solve and DACA and border security, that may be the best we can hope for,” Thune said, referring to the Obama-era Deferred Action for Childhood Arrivals program that Trump rescinded in September, putting hundreds of thousands of young immigrants at risk for deportation.

He clarified that he was speaking for himself instead of the entire Senate GOP conference.

Thune’s statement gives some support a fallback proposal that Sen. Rob Portman Robert (Rob) Jones PortmanRomney undecided on authorizing subpoenas for GOP Obama-era probes Congress needs to prioritize government digital service delivery House passes B bill to boost Postal Service MORE (R-Ohio) has floated privately to colleagues in recent days.

Portman has suggested passing a law to codify Obama’s 2012 executive order establishing DACA — which stopped short of giving illegal immigrants a pathway to citizenship — in exchange for beefing up border security.

Thune, however, noted that Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellMcConnell focuses on confirming judicial nominees with COVID-19 talks stalled McConnell accuses Democrats of sowing division by 'downplaying progress' on election security Warren, Schumer introduce plan for next president to cancel ,000 in student debt MORE (R-Ky.) has promised to bring an immigration bill to the floor after Feb. 8 under an open amendment process.

Congress has a March 5 deadline for finding a way to help DACA recipients, popularly known as "Dreamers."

“We agree with the president that we’ve got to deal with the issue of DACA. The question is, is it the much bigger, broader debate about immigration, which encompasses the other issues that have been attendant to that debate for a long time?” Thune said.

McConnell and Senate Democratic Leader Charles Schumer Chuck SchumerMcConnell accuses Democrats of sowing division by 'downplaying progress' on election security Warren, Schumer introduce plan for next president to cancel ,000 in student debt Schumer lashes out at Trump over 'blue states' remark: 'What a disgrace' MORE (N.Y.) discussed the outlines of the upcoming immigration debate before Tuesday’s State of the Union address, Thune said.

Thune told reporters that it does not appear leaders will reach an immigration deal by Feb. 8, when government funding is due to expire.

But Democrats are not expected to reject another short-term spending measure, forcing a shutdown, because McConnell has promised an open immigration debate.

Trump has insisted on Congress passing a four-point immigration proposal that gives Dreamers a 10- to 12-year path to citizenship, improves border security, limits family-based visas and ends the diversity visa lottery.

But Trump’s rhetoric at Tuesday’s State of the Union address irritated many Democrats, some of whom booed and hissed at his characterization of how family-based immigration works. Trump said it allowed immigrants to bring in an unlimited number of family members, which is not correct.

Schumer at a meeting with Democratic colleagues before the State of the Union urged his caucus to resist the four-point plan and instead rally behind a one-for-one trade of a DACA fix in exchange for stronger border security.

Thune praised Trump’s plan as a “good-faith offer” but argued that Democrats are opposed to it.

“My view is that ultimately a fallback position that can pass the House, the Senate and get signed would be DACA and border security, some sort of agreement between those two,” he said.

His comments Thursday indicate that some Senate Republicans, at least, would be willing to accept a more limited deal.

Other Republicans, such as Sens. David Perdue (Ga.) and James Lankford James Paul LankfordMcConnell works to lock down GOP votes for coronavirus bill Charities scramble to plug revenue holes during pandemic Warren calls for Postal Service board members to fire DeJoy or resign MORE (Okla.), who have been involved in immigration talks, however, say ending what they call “chain migration” and the visa lottery program must be part of any immigration deal.

And in the House, it could be more difficult to pass a deal that just covers DACA and border security.

The immigration talks are closely tied to talks on a measure to keep the government funded, however, and some have speculated that an immigration deal might eventually be paired with a longer-term spending bill.

Congress faces a Feb. 8 deadline to pass a measure to keep the government open.