Senators are discussing a scaled-back deal on immigration as they try to find an agreement that could get 60 votes in the Senate, under time pressure to make a deal.

A new proposal, which came up during a closed-door bipartisan meeting, would pair providing legal status to Deferred Action for Childhood Arrivals (DACA) recipients with a border security package.

But the limited agreement would leave out top priorities for both parties.

It wouldn't provide a path to citizenship for DACA recipients, who are young immigrants brought into the country illegally — a key ask for Democrats. It also wouldn't address changes to family-based immigration, a main requirement for conservatives.

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Senators coming out of the meeting downplayed their discussions, saying they are looking for ideas to pitch to Sens. John Cornyn John CornynCalls grow for Biden to expand election map in final sprint Bipartisan praise pours in after Ginsburg's death Chamber of Commerce endorses McSally for reelection MORE (R-Texas) and 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 (D-Ill.), who are in charge of drafting the Senate's base legislation. The two senators are the second-ranking members of their party in the upper chamber.

"You know, there have been no decisions made about what should be in the base bill. ... I think we should allow Sen. Cornyn and Sen. Durbin to let their process go forth before we start saying this must be in or this can't be in," Sen. Susan Collins Susan Margaret CollinsJeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Trump supporters chant 'Fill that seat' at North Carolina rally Momentum growing among Republicans for Supreme Court vote before Election Day MORE (R-Maine), who organized Thursday's meeting, told reporters.

A narrow deal that dealt only with DACA and border security wouldn't line up with the "four pillars" that a bipartisan group of lawmakers and President Trump Donald John TrumpUS reimposes UN sanctions on Iran amid increasing tensions Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Trump supporters chant 'Fill that seat' at North Carolina rally MORE agreed last month to use as a guide for the immigration bill.

Those parameters included a DACA fix, border security, limiting family-based immigration and getting rid of the diversity visa lottery.

But the scope of the changes to family-based immigration, or "chain migration," has emerged as a key sticking point. Democrats don't want the deal to address the issue at all, while conservatives want any changes to apply broadly to the immigrant population.

"What we're really trying to do is get results with regard to the issue in front of us, which are the children impacted by DACA and an opportunity to address the issue of border security," said Sen. Mike Rounds Marion (Mike) Michael RoundsChamber of Commerce endorses McSally for reelection Senate GOP eyes early exit Senate Republicans signal openness to working with Biden MORE (R-S.D.).

He added that a deal could go a step further than that by providing citizenship to the young immigrants but "then you also have to address the real thorny issue of chain migration."

"The straightforward solution is codify DACA. ... That doesn't make it a lot of people happy," he said.

Other senators described the various proposals under discussion as being aimed at trying to provide "symmetry" to both sides.

Asked what sort of bill he would write, if he were writing one, Sen. Marco Rubio Marco Antonio RubioSunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election Florida senators pushing to keep Daylight Savings Time during pandemic Hillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll MORE (R-Fla.) said it would be "limited" and "would deal with DACA and it would deal with border."

"The best way to think about it, guys, is that border equals DACA status. Citizenship equals chain migration," he said. "I think there's a general consensus that we want to start with a limited bill."

Thursday's meeting comes as senators have roughly two weeks to come up with an agreement on immigration that could be brought to the floor. The three-day government shutdown only ended when Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellMomentum growing among Republicans for Supreme Court vote before Election Day Trump expects to nominate woman to replace Ginsburg next week Video of Lindsey Graham arguing against nominating a Supreme Court justice in an election year goes viral MORE (R-Ky.) promised to bring up such legislation, in exchange for Democratic support for a spending bill that lasts through Feb. 8.

Trump threw the debate a curveball on Wednesday when he said he would support a path to citizenship. A senior administration official later clarified that it was a "discussion point."

The administration is expected to release an immigration proposal on Monday.

Trump kicked the immigration fight to Congress last year when Attorney General Jeff Sessions Jefferson (Jeff) Beauregard SessionsTrump's policies on refugees are as simple as ABCs Ocasio-Cortez, Velázquez call for convention to decide Puerto Rico status White House officials voted by show of hands on 2018 family separations: report MORE announced the administration would end the DACA program, which allows immigrants brought into the country illegally as children to work and go to school.

Congress has until March 5 to pass a fix or hundreds of thousands of illegal immigrants will be at risk of being deported.

Senators have proposed a myriad of legislative options, ranging from conservative proposals more in line with a wish list released in October to a "clean" bill that would provide a path to citizenship.

Asked if changes to "chain migration" — which allows citizens and permanent residents to sponsor family members — should be included in the Senate bill, GOP Sen. Lindsey Graham Lindsey Olin GrahamMomentum growing among Republicans for Supreme Court vote before Election Day Video of Lindsey Graham arguing against nominating a Supreme Court justice in an election year goes viral Warning signs flash for Lindsey Graham in South Carolina MORE (S.C.) said he would "rather do more than less."

"If you do it in two steps, where do you draw the line in step one?" he said. "If you do citizenship, you actually have to address that issue."

And it's unclear if Democrats would support a narrower deal that doesn't include a path to citizenship.

"You're going to see strong support on the Democratic side that you have to have some kind of path to citizenship. You're not going to be right of the president," said Sen. Amy Klobuchar Amy KlobucharThe Hill's Morning Report - Sponsored by The Air Line Pilots Association - White House moves closer to Pelosi on virus relief bill EPA delivers win for ethanol industry angered by waivers to refiners It's time for newspapers to stop endorsing presidential candidates MORE (D-Minn.), asked about the narrow option being floated.