WASHINGTON — Bargainers clashed Sunday over whether to limit the number of migrants authorities can detain, tossing a new hurdle before negotiators hoping to strike a border security compromise for Congress to pass this coming week. The White House wouldn’t rule out a renewed partial government shutdown if an agreement isn’t reached.

With the Friday deadline approaching, the two sides remained separated by hundreds of millions of dollars over how much to spend to construct President Donald Trump’s promised border wall. But rising to the fore was a related dispute over curbing Customs and Immigration Enforcement, or ICE, the federal agency that Republicans see as an emblem of tough immigration policies and Democrats accuse of often going too far.

Acting White House chief of staff Mick Mulvaney, in appearances on NBC’s “Meet the Press” and “Fox News Sunday,” said “you absolutely cannot” eliminate the possibility of another shutdown if a deal is not reached over the wall and other border matters. The White House had asked for $5.7 billion, a figure rejected by the Democratic-controlled House of Representatives, and the mood among bargainers has soured, according to people familiar with the negotiations not authorized to speak publicly about private talks.

“You cannot take a shutdown off the table, and you cannot take $5.7 (billion) off the table,” Mulvaney told NBC, “but if you end up someplace in the middle, yeah, then what you probably see is the president say, ‘Yeah, OK, and I’ll go find the money someplace else.'”

A congressional deal seemed to stall even after Mulvaney convened a bipartisan group of lawmakers at Camp David, the presidential retreat in northern Maryland. While the two sides seemed close to clinching a deal late last week, significant gaps remain and momentum appears to have slowed. Though congressional Democratic aides asserted that the dispute had caused the talks to break off, it was initially unclear how damaging the rift was. Both sides are eager to resolve the long-running battle and avert a fresh closure of dozens of federal agencies that would begin next weekend if Congress doesn’t act by Friday.

“I think talks are stalled right now,” Sen. Richard Shelby, R-Ala., said Sunday on “Fox News Sunday.” ”I’m not confident we’re going to get there.”

Sen. Jon Tester, D-Mont., who appeared on the same program, agreed: “We are not to the point where we can announce a deal.”

But Mulvaney did signal that the White House would prefer not to have a repeat of the last shutdown, which stretched more than a month, left more than 800,000 government workers without paychecks, forced a postponement of the State of the Union address and sent Trump’s poll numbers tumbling. As support in his own party began to splinter, Trump surrendered after the shutdown hit 35 days without getting money for the wall.

This time, Mulvaney signaled that the White House may be willing to take whatever congressional money comes — even if less than Trump’s goal — and then supplement that with other government funds.

“The president is going to build the wall. That’s our attitude at this point,” Mulvaney said on Fox. “We’ll take as much money as you can give us, and we’ll go find the money somewhere else, legally, and build that wall on the southern border, with or without Congress.”

The president’s supporters have suggested that Trump could use executive powers to divert money from the federal budget for wall construction, though it was unclear if he would face challenges in Congress or the courts. One provision of the law lets the Defense Department provide support for counterdrug activities.

But declaring a national emergency remained an option, Mulvaney said, even though many in the administration have cooled on the prospect. A number of powerful Republicans, including Senate Majority Leader Mitch McConnell, R-Ky., have also warned against the move, believing it usurps power from Congress and could set a precedent for a future Democratic president to declare an emergency for a liberal political cause.

The fight over ICE detentions goes to the core of each party’s view on immigration.

Republicans favor tough enforcement of immigration laws and have little interest in easing them if Democrats refuse to fund the Mexican border wall. Democrats despise the proposed wall and, in return for border security funds, want to curb what they see as unnecessarily harsh enforcement by ICE.

People involved in the talks say Democrats have proposed limiting the number of immigrants here illegally who are caught inside the U.S. — not at the border — that the agency can detain. Republicans say they don’t want that cap to apply to immigrants caught committing crimes, but Democrats do.

In a series of tweets about the issue, Trump used the dispute to cast Democrats as soft on criminals. He charged in one tweet: “The Border Committee Democrats are behaving, all of a sudden, irrationally. Not only are they unwilling to give dollars for the obviously needed Wall (they overrode recommendations of Border Patrol experts), but they don’t even want to take muderers into custody! What’s going on?”

Democrats say they proposed their cap to force ICE to concentrate its internal enforcement efforts on dangerous immigrants, not those who lack legal authority to be in the country but are productive and otherwise pose no threat. Democrats have proposed reducing the current number of beds ICE uses to detain immigrants here illegally from 40,520 to 35,520.

But within that limit, they’ve also proposed limiting to 16,500 the number for immigrants here illegally caught within the U.S., including criminals. Republicans want no caps on the number of immigrants who’ve committed crimes who can be held by ICE.

As most budget disputes go, differences over hundreds of millions of dollars are usually imperceptible and easily solved. But this battle more than most is driven by political symbolism — whether Trump will be able to claim he delivered on his long-running pledge to “build the wall” or newly empowered congressional Democrats’ ability to thwart him.

Predictably each side blamed the other for the stall in negotiations.

“We were, you know, progressing well,” Rep. Tom Graves, R-Ga., said Sunday on ABC’s “This Week.” ”I thought we were tracking pretty good over the last week. And it just seems over the last 24 hours or so the goalposts have been moving from the Democrats.”

House Budget Committee Chairman John Yarmuth, D-Ky., countered by telling the same show, “The numbers are all over the place.”

“I think the big problem here is this has become pretty much an ego negotiation,” Yarmouth added. “And this really isn’t over substance.”