WATCH LIVE: The Senate meets as lawmakers consider a deal to fund Homeland Security

WASHINGTON (AP) — Senators are debating a proposal to end the Homeland Security budget gridlock by funding much of the department, including TSA airport workers who work without pay, but excluding ICE enforcement and removal operations that have been at the heart of the dispute.

The Senate reconvenes at 12 noon EST. Watch the live stream in our video player above.

This potential breakthrough came after a group of Republican senators headed to the White House late Monday to meet with President Donald Trump. Senators said they expected negotiators to work through the night to hammer out details and provide written proposals for both parties to discuss Tuesday at their weekly group lunches.

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“All I can say is that the discussions were very positive and productive, and I hope they go in the right direction,” Senate Majority Leader John Thune said.

“Both sides are working in a serious way,” Senate Democratic Leader Chuck Schumer told reporters late in the evening.

The sudden turn in a month-long standoff with long lines congested U.S. airports after routine funding for the Department of Homeland Security was cut, leaving the Transportation Security Administration understaffed during the spring travel season. Democrats refuse to fund Homeland Security without restrictions on Trump’s immigration enforcement operations and mass deportations after the deaths of US citizens during Immigration and Customs Enforcement protests in Minneapolis.

Senate Republicans will hold a briefing while lawmakers consider a potential funding deal for the Department of Homeland Security.

Trump took the unusual step over the weekend when he ordered Immigration and Customs Enforcement officers to provide security at the airport, worrying some lawmakers that it could escalate tensions.

He watches: The Senate voted to confirm Markwayne Mullen as Secretary of the Department of Homeland Security

The contours of the deal under consideration would fund most of the Department of Homeland Security, but excludes funding for one key part of ICE — the enforcement and removal operations that are central to Trump’s deportation agenda.

Under the proposed package, ICE’s Homeland Security Investigations would be funded as well as Customs and Border Protection, but with new guardrails to put officers from those departments in their traditional roles, rather than more recently used in immigrant arrest sweeps in cities. It would also include a number of changes to immigration processes that Democrats have called for, including requiring officers to wear body cameras and ID cards.

Senate Republicans will hold a briefing while lawmakers consider a potential funding deal for the Department of Homeland Security.

Since much of ICE is already funded by Trump’s large tax relief bill, and immigration workers are still receiving salaries during the partial government shutdown, the senators said the new restrictions would also be imposed on operations that rely on that funding source as well.

Read more: Federal immigration agents were deployed to the Atlanta airport during the partial closure

“I’m going to work all night,” said Republican Sen. Katie Britt of Alabama, the chief negotiator who returned from the White House meeting hoping they had a solution to “landing this plane.”

“We will work hard,” she added.

Senator Chris Coons, Democrat of Delaware, who was not part of the group at the White House, said his understanding is that there is a “sense of urgency” coming from the talks.

Coons described different options for senators at this point — from no money at all for ICE but also no restrictions on the agency’s operations, to fully funding ICE but with more restrictions demanded by Democrats, to a compromise option of funding most of DHS except for ICE enforcement and removal operations. This middle option is what he and other senators understood was widely on the table after the White House talks.

He watches: Trump rejects Senate proposal to reopen Department of Homeland Security without funding ICE

“The first step is to get the proposal in writing,” said Sen. Angus King, an independent from Maine. “I want to see exactly what that means.”

Senators also confirmed late Monday the appointment of Markwayne Mullen as Secretary of Homeland Security. He takes over for Kristi Noem, who led the administration’s immigration enforcement operations that erupted with public outcry and a funding crisis.

Mullen offers a possible new facet of the migration process. During his confirmation hearing last week, Mullen touched on another key demand Democrats want: ensuring a judge signs off on search warrants that immigration officers use to search people’s homes, rather than simply relying on administrative search warrants issued by the department.

“This is important,” Senator Peter Welch, Democrat of Vermont, said of the progress toward the changes. “Noem’s gone. This is a big deal.”

Sen. John Hoeven, R.N.D., said he hopes senators can work things out. “Look, there are a lot of different variables in the equations,” he said. “I hope we get there.”

Associated Press writer Seung-Min Kim contributed to this report.