A top White House official warned Sunday that it's "very possible" the partial government shutdown stretches into the new year and that how quickly numerous shuttered Cabinet departments and agencies resume doing the people's business is up to Congress.

"The ball is in the Senate's court," acting White House chief of staff Mick Mulvaney said.

Senate Democrats, who oppose funding for President Donald Trump's promised border wall, contend government could reopen immediately if Trump drops his demand to extend a physical barrier along the U.S.-Mexico border.

A stalemate over the wall led parts of the government to shut down Saturday after funding for numerous departments and agencies expired.

Mulvaney, who is also director of the White House budget office, said he's awaiting word from Senate Democratic leader Chuck Schumer of New York after the administration on Saturday presented Schumer with a counteroffer in the long-running dispute over funding the wall.

Mulvaney withheld specifics but placed the offer between Trump's $5.7 billion request and $1.3 billion offered by Democrats.

The shutdown was expected to last through Thursday after the House and Senate, which held rare weekend sessions, adjourned until later in the week. Monday and Tuesday, Christmas Eve and Christmas, respectively, are federal holidays, meaning much of the federal government would already be closed.

Wednesday is the first day taxpayers could begin to feel the effects of a shutdown, Mulvaney said. But he predicted it could last beyond Thursday, when Congress is next scheduled to come into session.

"It's very possible that this shutdown will go beyond the 28th and into the new Congress," he said.

Democrats held firm Sunday in opposition to paying for a border wall, which was a central promise of Trump's campaign for president.

Sen. Jeff Merkley, D-Ore., said the administration is sitting on most of the money Congress gave Trump last year for border security, excluding a wall.

"If you're not going to spend nine out of 10 dollars on an issue, you obviously don't care about it that much," Merkley said. "This is politics, not policy."

Mulvaney countered that "the president's not going to not accept money for a border wall."

On the second day of the federal closure, Trump tweeted Sunday that what the country needs is "a good old fashioned WALL that works," as opposed to aerial drones and other measures that "are wonderful and lots of fun" but not the right answer to address "drugs, gangs, human trafficking, criminal elements and much else from coming into" the United States.

From coast to coast, the first day of the shutdown played out in uneven ways. The Statue of Liberty remained open for tours, thanks to money from New York state, and the U.S. Postal Service, an independent agency, was still delivering mail.

Yet the disruption has affected many government operations and the routines of 800,000 federal employees. Roughly 420,000 workers were deemed essential and were expected to work unpaid. An additional 380,000 were to be furloughed, meaning they will stay home without pay. The Senate had already passed legislation ensuring that workers will receive back pay, and the House was likely to follow suit.

Unlike past shutdowns, this one seemed to lack urgency, coming during the long holiday weekend after Trump had already declared Christmas Eve a federal holiday. Rather than work around the clock to try to end the shutdown, as they had done in the past, the leaders of the House and the Senate effectively closed up shop. But they didn't rule out action if a deal were struck.

"Listen, anything can happen," Senate Majority Leader Mitch McConnell told reporters after he closed the Senate's rare Saturday session hours after it opened.

But after ushering Vice President Mike Pence through the Capitol for another round of negotiations, Sen. Richard Shelby, R-Ala., chairman of the Appropriations Committee, said a quick end to the shutdown was "not probable."

Trump had lunch at the White House on Saturday with conservative lawmakers. Absent were GOP leaders or Democrats who would be needed for a deal. The White House said Trump would spend Christmas in Washington because of the shutdown and that his wife, first lady Melania Trump, would fly back from their Florida estate to spend the holiday with him.

With Democrats set to take control of the House on Jan. 3, and House Speaker Paul Ryan, R-Wis., on his way out, the shutdown was providing a last gasp of the conservative majority before the new Congress.

Trump savored the prospect of a shutdown over the wall for months. This past week he said he would be "proud" to close down the government. He had campaigned on the promise of building the wall, and he also promised Mexico would pay for it. Mexico has refused.

In recent days, though, Trump tried to shift blame to Democrats for not acceding to his demand. He has given mixed messages on whether he would sign any bill into law.

Schumer and Pence met Saturday at the request of the White House, according to Schumer's office. But the senator's spokesman said they remained "very far apart" on a spending agreement.

Schumer said the "Trump shutdown" could end immediately if the president abandons the wall.

Democrats said they were open to proposals that didn't include the wall, which Schumer said was too costly and ineffective. They have offered to keep spending at existing levels of $1.3 billion for border fencing and other security.

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 as Trump faced criticism from conservatives for "caving" on a campaign promise, he pushed the House to approve a package temporarily financing the government but also setting aside $5.7 billion for the border wall.

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.

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. 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.

Mulvaney appeared on "Fox News Sunday" and ABC's "This Week." Merkley also appeared on ABC.

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Associated Press writers Alan Fram, Mary Clare Jalonick and Jill Colvin in Washington contributed to this report.