Vice President Mike Pence arrived on Capitol Hill with a counter-offer to Democrats after the two sides traded offers in recent days. At the White House, Trump heard mixed messages during a lunch with conservative lawmakers; some wanted him to fight for the wall, others preferred to get the government re-opened. The Senate, which had gaveled in with the House for a rare weekend session, adjourned until Christmas Eve, but won't return for a full session until Dec. 27.
Even a temporary measure to keep government running for a few days while negotiations continued seemed out of reach.
"Listen, anything can happen," Senate Majority Leader Mitch McConnell told reporters after he closed the session.
But the situation seemed less hopeful for a resolution. The Republican chairman of the Appropriations Committee, Sen. Richard Shelby of Alabama, said a quick end to the shutdown was "not probable."
"I don't think it's imminent we're going to reach a deal," Shelby told reporters after he ushered Pence through the halls for meetings. "I wish we could."
Trump was demanding $5 billion for a wall, but congressional Democrats were refusing to accede in a stalemate that provided a chaotic coda for Republicans in the waning days of their two-year reign controlling government.
The president jettisoned his Florida holiday getaway to his club Mar-a-Lago, tweeting, "I am in the White House, working hard."
Trump hosted a lunch with conservative lawmakers, including House Freedom Caucus chiefs Mark Meadows of North Carolina and Jim Jordan of Ohio, and several senators, among them Lindsey Graham of South Carolina. Absent from the guest list were GOP leaders or any Democrats.
For the second day in a row, Pence shuttled over to the Capitol to work on a deal. Senate Democratic leader Chuck Schumer of New York met with Pence at the request of the White House, according to Schumer's office.
Shelby said the two sides had exchanged counter-offers over the past days and that Pence was arriving with a new one from the White House. Pence left a short time later.
Schumer said the "Trump shutdown" could end immediately if Trump simply dropped his demand for money that was the centerpiece of his presidential campaign. Trump had pledged that Mexico would pay for the wall; Mexico has refused.
"If you want to open the government, you must abandon the wall," Schumer said.
Democrats said they were open to other proposals that don't include the wall, which Schumer said was too costly and unpopular. They have offered to keep spending at existing levels of $1.3 billion for border fencing and other security.
But Trump, digging in, tweeted about "the crisis of illegal activity" at American's southern border is "real and will not stop until we build a great Steel Barrier or Wall."
Republican leaders largely stayed in the background of the negotiations, and McConnell opened the Senate saying any deal to reopen government would require Democratic support for passage and the president's signature.
The impasse blocked money for nine of 15 Cabinet-level departments and dozens of agencies, including the departments of Homeland Security, Transportation, Interior, Agriculture, State and Justice.
The disruption affected many government operations and the routines of 800,000 federal employees. Roughly 420,000 workers were deemed essential and will work unpaid just days before Christmas. An additional 380,000 will be furloughed, meaning they will stay home without pay.
Federal employees already were granted an extra day of vacation on Monday, Christmas Eve, thanks to an executive order that Trump signed this past week. The Senate passed legislation ensuring that workers will receive back pay. The House seemed sure to follow suit.
Late Friday, Pence, Trump son-in-law and senior adviser Jared Kushner and White House budget chief Mick Mulvaney left the Capitol late after hours of bargaining with congressional leaders produced no apparent compromise.
Mulvaney sent agency heads a memorandum telling them to "execute plans for an orderly shutdown." He wrote that administration officials were "hopeful that this lapse in appropriations will be of short duration."
Those being furloughed included nearly everyone at NASA and 52,000 workers at the Internal Revenue Service. About 8 in 10 employees of the National Park Service were to stay home; many parks were expected to close.
Some agencies, including the Pentagon and the departments of Veterans Affairs and Health and Human Services, were already funded and will operate as usual.
The U.S. Postal Service, busy delivering packages for the holiday season, were not affected because it's an independent agency. Social Security checks were mailed, troops remained on duty and food inspections continued.
Also still functioning were the FBI, the Border Patrol and the Coast Guard. Transportation Security Administration officers continued to staff airport checkpoints and air traffic controllers were on the job.
Trump has savored the prospect of a shutdown over the wall for months. Last week he said he would be "proud" to close down the government. Many of Congress' most conservative Republicans welcomed such a confrontation, but most GOP lawmakers wanted to avoid one because polling showed the public opposed the wall and a shutdown over it.
Initial Republican reaction to the shutdown was muted. Sen. Lamar Alexander of Tennessee said, "This is a complete failure of negotiations and a success for no one."
Trump made clear last week that he would not blame Democrats for any closure. However, he and his GOP allies spent the past few days saying Democrats, who take control of the House on Jan. 3, bore responsibility.
Senators approved a bipartisan deal earlier in the week to keep the government open into February and provide $1.3 billion for border security projects, but not the wall. But the House rebelled and approved a package temporarily financing the government but also setting aside $5.7 billion for the border wall.
A test vote in the Senate on Friday showed that Republicans lacked the 60 votes needed to advance the House plan.
Associated Press writers Alan Fram, Mary Clare Jalonick and Jill Colvin in Washington contributed to this report.
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