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.

The president plans to hold a rally Monday in El Paso, Texas, at the U.S. border with Mexico, to show why he's demanding more than 100 miles of new walls, costing $5.7 billion, along the 1,900-mile border, despite opposition from Democrats and some Republicans in Congress.

But rising to the fore of negotiations Sunday 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.

And the mood among bargainers has soured, according to people familiar with the negotiations not authorized to speak publicly about private talks.

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.

"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 and sent Trump's poll numbers tumbling. Trump yielded after the shutdown hit 35 days.

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 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.