Updated Feb. 15 at 8:30 a.m. ET

Prospects for a Senate immigration bill appear dim, as lawmakers fear they won’t be able to craft a single bill that can pass with bipartisan support and still win the support of President Trump, which is necessary for the House to consider any legislation passed by the Senate.

Senators scrambled behind the scenes to try to rally support for a bipartisan compromise on Wednesday, ahead of a deadline set by Senate Majority Leader Mitch McConnell, R-Ky., to finish immigration by the end of the week. But the mood was dour after the White House rejected any legislation that does not further limit legal immigration, and lawmakers aim to start leaving town for a week-long recess on Thursday night.

Trump threw his support behind a GOP-written bill sponsored by Senate Judiciary Committee Chairman Chuck Grassley, R-Iowa, to give 1.8 million immigrants in the country illegally who arrived as children a chance to apply for citizenship. That would be in exchange for limits to legal immigration through ending the visa lottery system and cutting family-based immigration policies, which the president and many conservatives refer to as “chain migration.”

Trump said he would reject any bill that does not meet his four pillars: “A lasting solution on DACA, ending chain migration, cancelling the visa lottery, and securing the border through building the wall and closing legal loopholes.”

“I am asking all senators, in both parties, to support the Grassley bill and to oppose any legislation that fails to fulfill these four pillars,” Trump said in a statement. “That includes opposing any short-term ‘Band-Aid’ approach.”

The bipartisan legislation released Wednesday night has the support of at least 16 Senators—well short of the 60 needed for it to pass. That plan includes a 12-year path to citizenship for all DACA eligible immigrants, $25 billion in border security spending and limits on which family members the beneficiaries can sponsor for citizenship.

The plan was written by a small bipartisan group including Sens. Susan Collins, R-Maine, Joe Manchin, D-W.Va., and Lindsey Graham, R-S.C. It is said to narrowly focus on those DACA recipients. Details of the legislation remained hazy as senators worked to rally co-sponsors for the bill.

The bill’s main sponsor, Sen. Mike Rounds, R-S.D., said the legislation is a moderate solution but he does not think the bill can pass. Rounds told NPR’s Steve Inskeep he doesn’t think the Grassley bill, known as the chairman’s mark, can succeed either.

“I don’t think the chairman’s mark will receive enough votes from both sides of the aisle to pass,” Rounds said. “I think ours, if it had been offered last probably would have garnered more than 60 votes to move forward to be a vehicle to actually get something done.”

Sen. David Perdue, R-Ga., a close ally of President Trump, told reporters he does not expect the White House to budge and support anything less.

“If you do something much narrower than what we’ve got proposed, you’ll be right back here in four or five years doing the same thing again with another wave,” Perdue said. “If you don’t break the chain migration issue, you’re going to be back here because you’re reinstating another wave of parents who will smuggle their kids in illegally.”

Many Democrats and some Republicans say they want to focus on granting rights to those immigrants who are in the country illegally after being brought in as children. Roughly 700,000 of those immigrants stand to lose legal protections starting on March 5, the date that the White House has established for the beginning of the sunset on the Deferred Action for Childhood Arrivals program (DACA), established by President Obama.

Senate leaders have set up a process to allow votes on a variety of proposals, including the Grassley bill. They would vote on the emerging bipartisan bill and a second narrow bill written by Sens. Chris Coons, D-Del., and John McCain, R-Ariz., to address the DACA population. Coons said Wednesday that his proposal is a starting point that can be adapted by adding specific amendments that have the support of a majority of Senators.

“If we can make more progress, if we can attract more bipartisan support through amendments or revisions, I welcome that,” Coons said on the Senate floor. “We can find a way forward together.”

But leaders have been unable to reach an agreement to start that debate or hold votes while senators are still at odds of which bills they support.

Some in Congress privately fear that Trump’s emphatic support for the Grassley bill could scare off Republicans who might otherwise support a bipartisan compromise. House Speaker Paul Ryan, R-Wis., says he will only bring up legislation that has Trump’s full support. Republican senators are unlikely to take a political risk in voting for a bipartisan bill if they believe that it is destined for failure in the House.

A 2013 bill to massively overhaul the immigration system passed the Senate overwhelmingly, but was never taken up by the GOP-controlled House in the face of fierce opposition from conservative hard-liners.

Tensions were high throughout the day on Wednesday as senators rallied around Trump’s demands. A visibly frustrated Grassley vented to reporters that Democrats needed to drop their opposition to the family-related portions of the bill and embrace the only offer Trump has embraced.

“The Democrats have been pleading for months and months and months for justice on this,” Grassley said. “Now you’ve got a compassionate president who has gone way beyond what they ever thought he would do. Why would they turn it down?”

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