WASHINGTON — The battle in Congress over the number of detention beds under the control of Immigration and Customs Enforcement has pushed the border security fight beyond the symbolism of a wall to the core of the immigration debate — how the nation’s laws are to be enforced far beyond the border with Mexico.

The impasse over President Donald Trump’s roundups and detention of immigrants without legal authorization has stalled progress on a bipartisan deal to avert a second government shutdown this Saturday, even after Trump reluctantly accepted far less money than he wanted for repairs and extensions of existing border barriers — and no new wall. The Republican and Democratic leaders of the House and Senate Appropriations committees were again meeting Monday night, determined to nail down a final agreement before funds run out at week’s end.

And aides in both parties warned that a final deal might leave the number of detention slots — or “interior beds” — unchanged, not reduced as Democrats want and not increased as Trump wants.

But for now, House Democrats, urged on by immigration rights group, are pushing hard, hoping to leverage White House fears of another damaging shutdown into a softening of the president’s hard-line immigration policies that they say have torn apart families, wrenched productive citizens from the communities they have lived in for years and infused a heartlessness into official U.S. immigration policy.

The Democrats’ tool: limit the number of beds that ICE has to hold immigrants without legal authorization in custody to 16,500 from around 20,700.

The Democrats’ ultimate goal is to cut the overall number of detention beds, including those occupied by asylum-seekers and people caught at the border, from its current level of around 49,000 to 34,000, the number funded during the Obama administration, Democratic aides said. That, they say, would end sweeps and roundups, and force ICE to focus on pursuing hardened criminals.

Last year, the Trump administration requested funding for 52,000.

With their number, Democrats say they can seize the initiative on immigration from a president who has staked his political fortunes on the issue.

“We started at zero on the wall, and we compromised a lot after that, and we are now asking them to change, too,” said Rep. Lucille Roybal-Allard, D-Calif., a member of the 17-member House and Senate conference committee tasked with hammering out a compromise.

Trump was catching on. When Sen. Richard Shelby, R-Ala., chairman of the Appropriations Committee, presented him with the Democrats’ demand, he rejected it quickly and said he would rather shut the government down than agree, according to two people briefed on the exchange.

“These are people coming into our country that we are holding and we don’t want in our country,” the president told reporters at the White House late Monday. “That’s why they don’t want to give us what we call ‘the beds.’ It’s much more complicated than beds, but we call them from ‘the beds.'”

In private, Republicans responded with a plan that would exempt many detained immigrants from the cap, including those people either charged with or convicted of crimes, including misdemeanor drug offenses and violent felonies. That, in turn, was rejected by Democrats.

“You have ICE agents picking up mothers and fathers and children in their own neighborhoods. That’s why the beds issue is so much important than the wall,” said Roybal-Allard, whose Los Angeles-area district is 85 percent Hispanic, the highest percentage of any district in the country.

The number of beds occupied by detainees fluctuates over time, influenced by a variety of factors, including ICE enforcement policies and the flow of migrants at the border with Mexico. The rate of that flow is unpredictable and determined by factors such as the performance of the economies north and south of the border, crime, gang activity and the business practices of coyotes paid to transport migrants from Mexico and Central America to California and the Southwest.

The number of monthly apprehensions of migrants at the border has averaged 25,000 to 40,000 for most of the past decade, but has risen to about 50,000 over the past several months, according to statistics compiled by the Department of Homeland Security.

If ICE does not have enough room to place individuals and family members they detain, they must loosen their enforcement actions, creating a powerful motive for new migrants to enter the country illegally, Trump administration officials say.

“You cannot have border security, without strong interior enforcement, whether there is a wall there or not,” said Matt Albence, deputy director of ICE, on Monday in a conference call with reporters.

Republicans closed ranks to blast the plan.

“This is a poison pill that no administration, not this one, not the previous one, should ever accept,” Sen. Mitch McConnell, R-Ky., the Senate majority leader, said on the Senate floor. “Imagine the absurdity of this: House Democrats want to set a limit on how many criminal aliens our government can detain.”

By 7 p.m. Monday, the chairmen and ranking members from the House and Senate Appropriations committees had met privately twice and were planning a third meeting to see if they could find some way to overcome the impasse over the beds. They told reporters that they were working to prevent another government shutdown, but had yet to reach any conclusions.

“We haven’t resolved anything,” said Rep. Nita Lowey, D-N.Y., chairwoman of the House Appropriations Committee. “We’re going to continue to talk.”

Shelby told reporters: “We’re trying to do our jobs. That’s all we can tell you.”

“At the moment,” he added, “I think the odds have improved, but they still have not crystallized.”

If a deal is not reached, Congress could pass another short-term, stopgap spending bill to keep the funds flowing and the talks on track. But for the time being, the lead negotiators declined to entertain that prospect and remained optimistic for a solution.

“Do you really think I’m going to make a guesstimate of that?” Lowey said, when asked about how long a potential bill would be.

And Sen. Patrick Leahy, D-Vt., the ranking member of the Senate Appropriations Committee, insisted that both he and Shelby thought it was preferable to find a resolution by the end of the night and not let the impasse languish any longer.

“We’re trying to be legislators,” he said.

On Monday, Democratic leadership aides said that there would be no deal without some concession on the bed issue — in part because immigrants rights groups and party liberals would revolt if they agreed to extend border barriers without getting something tangible in return.

Last Friday, when word of a possible deal first leaked out, advocates for immigrants reached out to Democratic leadership offices, including House Speaker Nancy Pelosi’s, to say that they would oppose any deal that did not address their concerns about ICE.

“For the last two years, we have been trying to limit the bad. We have taken a defensive approach, but now House Democrats have the power to start doing some good,” said Lorella Praeli, deputy national political director of the American Civil Liberties Union, one of the groups that has pressed the Democratic leaders, Pelosi of California and Sen. Chuck Schumer of New York, to reject any deal that does not include steps to reduce aggressive immigration enforcement.

“It’s time for them to show that they are fighting for us,” Praeli added. “It means you have to do something more than a floor speech or a tweet supporting immigrants. It’s time to actually do something.”

This article originally appeared in The New York Times.