The White House offered additional immigration enforcement concessions to Democrats Friday evening as border czar Tom Homan met a second time with a bipartisan group of senators seeking to end the Homeland Security shutdown, according to lawmakers who attended.

Leaving the private meeting, Republican senators said they hope Democrats respond over the weekend to the Trump administration’s bolstered proposal of immigration enforcement changes meant to address Democratic demands for funding DHS.

“We need to get the government back open,” Homan said as he left the meeting. “It was a good discussion. That is all I’m going to say.”

Washington Sen. Patty Murray, the Senate’s top Democratic appropriator, was in attendance, along with Democratic Sens. Maggie Hassan of New Hampshire, Catherine Cortez Masto of Nevada and Angus King of Maine, an independent who caucuses with Democrats.

Those senators declined to comment as they left the confab. But a Democratic aide familiar with the meeting said there is “a ways to go” in the ongoing negotiations “to secure the significant reforms that Democrats have laid out for weeks and that are necessary to earn the support of the Democratic caucus.”

Sen. John Hoeven (R-N.D.), who also attended, said afterward he thinks the group “made some more progress” toward a deal as the DHS shutdown approaches five weeks. Senate Appropriations Chair Susan Collins (R-Maine) said the White House had made “a very fair, reasonable offer.”

“I think Democrats need to come back to us now and talk to us about what they’re willing to do,” Hoeven added. “We’ve put so many things on the table and put them out.”

An ongoing complaint about the negotiations from Democrats has been that Republicans and the White House have offered their proposals in recent weeks without legislative text. But Republicans offered fresh draft legislation Friday, put together by the White House, according to Hoeven.

He characterized the latest GOP offer as “building” on a letter the White House sent earlier this week and “providing more detail on it and providing legislative text on it.”

Sen. Katie Britt (R-Ala.), chair of the Homeland Security funding panel, said as she left the meeting that a deal to reopen DHS needs to be clinched by next week “one way or the other.”

“There has to be a pathway forward,” she said

The group of lawmakers is hoping to meet again over the weekend, with the Senate planning to be in session both Saturday and Sunday working on other legislative priorities. But Republicans said timing will be up to Democrats, who are now expected to respond with a counteroffer.

Democrats have insisted on requiring judicial warrants for immigration raids, and that remains unsettled, but Hoeven said there was room for agreement over creating “serious” criminal penalties for “doxxing” and harassing law enforcement.

That could help ease concerns about requiring DHS officers to identify themselves and their agency when conducting immigration enforcement operations, though Hoeven said the masking ban Democrats want remains a nonstarter.

“ICE is going to have to be able to wear masks the same way other law enforcement does,” he said.

A meeting is now underway seeking potential paths for ending the shutdown of the Department of Homeland Security.

Tom Homan, President Donald Trump’s border czar, is meeting with top Senate appropriators and other key senators. It’s the second meeting of the same group in as many days.

Speaker Mike Johnson is planning to put a stalled Homeland Security funding bill on the House floor a third time next week, according to three people granted anonymity to discuss private plans, as the GOP moves to further pressure Democrats to end the five-week closure.

Two versions of the bill have already passed the House, each time with just a few House Democrats breaking from party lines to back it. But the bill is still held up in the Senate, where Democrats have refused to approve DHS funding without adding new restrictions on immigration enforcement.

The House will also vote on a resolution next week in support of DHS workers, including TSA officers who have gone without pay as the spring break travel crush stresses U.S. airports.