Senate Democratic Leader Chuck Schumer, D-N.Y., called on President Trump to "abandon the wall" Saturday if he wants to reopen the government, saying Trump does not have the votes in the Senate to get it funded -- hours after the government shut down over an impasse over funding for Trump's signature 2016 campaign promise.

"It will never pass the Senate, not today, not next week, not next year. So President Trump, if you want to open the government, you must abandon the wall, plain and simple," Schumer said on the Senate floor.

The partial shutdown began at midnight Saturday, a few hours after the House and Senate adjourned without getting a funding agreement to the president's desk. The shutdown was expected to last at least a few days, with sources on both sides of the aisle telling Fox News that Washington could be in for a prolonged shutdown.

The Senate adjourned Saturday afternoon and was not due to meet for a scheduled session until Thursday. Early Saturday evening, the House also concluded for the day.

Vice President Mike Pence and Acting Chief of Staff Mick Mulvaney arrived at the Capitol Saturday afternoon to meet with Schumer to continue negotiations for an end to the stalemate. Senate Majority Leader Mitch McConnell, R-Ky., said that "productive discussions are continuing."

"When those negotiations produce a solution that is acceptable to all parties -- which means 60 votes in the Senate, a majority in the House, and a presidential signature -- at that point, we will take it up here on the Senate floor," he said.

Late Saturday afternoon, a Schumer spokesman said that "the vice president came in for a discussion and made an offer. Unfortunately, we're still very far apart."

In a letter addressed to fellow Democratic colleagues on Saturday, House Minority Leader Nancy Pelosi, D-Calif., wrote that "Last night, Republicans shut down the government." She added that barring any developments, making "progress to end the Trump Shutdown in the next several days" was not anticipated.

"Until President Trump can publicly commit to a bipartisan resolution, there will be no agreement before January when the new House Democratic Majority will swiftly pass legislation to re-open government," Pelosi wrote, before expressing her wishes for a happy holiday.

With the standoff grinding on, the White House revealed on Saturday that the president planned to stay in the nation's capital over the holiday.

“Due to the shutdown, President Trump will remain in Washington, D.C. and the First Lady will return from Florida so they can spend Christmas together,” White House Press Secretary Sarah Sanders said in a statement.

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The main sticking point for negotiations was funding for Trump's signature 2016 campaign promise of a wall on the southern border. Trump had demanded $5.7 billion for wall funding, and a bill with that funding attached passed the House on Friday. But efforts have derailed in the Senate, where 60 votes were required for passage, and therefore Democrat votes are needed in conjunction with support by the GOP.

Democrats have poured cold water on the idea that they would support anything close to that. Schumer, in his remarks Saturday, said that the wall was a "bone to the hard right" and that they had proposed $1.3 billion for "border security."

"I’ve heard the president and his allies in the media say that Democrats don’t support border security. Nothing could be further from the truth. Democrats have always been for smart and effective ways to secure our border," he said. "We are pushing for technology, like drones and sensors, and inspection equipment."

McConnell accused Democrats of backing away from past support for border security, and said they were rejecting a "reasonable request" for the $5 billion in funding.

"They’ve refused to meet President Trump halfway and provide even one-fifth of the resources for the border they were willing to provide just a few months ago," he said on the Senate floor.

Trump has been keen to blame Democrats for the impasse and on Friday urged McConnell to invoke the so-called “nuclear option” which would change Senate procedure to require only a simple majority to approve the bill -- therefore allowing Republicans to override Democratic objections.

“Mitch, use the Nuclear Option and get it done! Our Country is counting on you!” he tweeted on Friday.

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Late Friday he emphasized the need for a wall in a video he posted to Twitter, and he blamed the shutdown on the Democrats.

“We’re going to have a shutdown, there’s nothing we can do about that because we need the Democrats to give us their votes,” he said. “Call it a Democrat shutdown, call it whatever you want, but we need their help to get this approved.”

That contrasted with remarks he made last week during an explosive Oval Office face-off with Schumer and Pelosi, in which he said he was "proud" to shut down the government for border security.

"I will take the mantle. I will be the one to shut it down. I’m not going to blame you for it,” he said.

On Saturday, Trump held a lunch at the White House to discuss border security with staff and top conservatives including Reps. Mark Meadows, R-N.C., Jim Jordan, R-Ohio, Matt Gaetz, R-Fla., Sen. Lindsey Graham, R-S.C., and Sen. Mike Lee, R-Utah. The inclusion of some of the more hardline voices on immigration could likely serve to harden Trump's resolve against backing down on the wall.

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The Senate appropriations bill passed on Wednesday is the base bill for funding, and that allocated $1.6 billion for border security. But it did not spend all money available under sequestration caps. There is an extra $900 million available, that could theoretically go toward funding the wall. If that was allocated, it could offer Trump a total wall/border package of about $2.5 billion.

While there appeared to be little movement on Saturday, Sunday was expected to be a key day for negotiations to end the shutdown. Lawmakers were aiming for a tentative agreement on all seven outstanding appropriation bills, to be funded until the end of September 2019. A senior source close to the negotiations told Fox News that they will aim to “see by Sunday morning if there is a center of gravity” for nailing down a deal.

Fox News is told Trump would accept the increase in wall funding, and that the administration believes it can find additional wall money across various federal programs that could be “reprogrammed” for the wall. White House Press Secretary Sarah Sanders said on "America's Newsroom" this week that there were "other ways that we can get to that $5 billion."

Congress has a little bit of wiggle room for movement as it has a weekend, followed by Christmas Eve -- for which Trump has given federal workers a day off -- and then Christmas Day. So that means that the partial shutdown will not fully bite until Wednesday.

About one-quarter of the government will be affected in a shutdown. Nine of the 15 Cabinet-level departments are to shutter, along with dozens of agencies. Those departments are: Agriculture, Commerce, Homeland Security, Housing and Urban Development, Interior, Justice, State, Transportation and Treasury.

Essential personnel would still be required to work but without pay. Nearly 90 percent of the Homeland Security staff is deemed essential.

Roughly 420,000 workers will be deemed essential and will work unpaid, while more than 380,000 people will be furloughed in the shutdown – meaning they will experience a temporary leave from their work

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This will include most of NASA, Housing and Urban Development, Commerce and National Park Service workers. Additionally, about 52,000 IRS workers would be furloughed.

The U.S. Postal Service (USPS) will remain open as usual during a partial government shutdown because it is “an independent entity that is funded through the sale of our products and services, and not by tax dollars,” a spokesman told Fox News.

TSA agents, air traffic controllers and border security agents also will be required to work through a shutdown – albeit they might not get a paycheck right away.

Amtrak, a government-owned corporation, also will continue with normal operations during a short-term shutdown, a spokeswoman confirmed to Fox News.

Members of Congress will continue to be paid, as legislative branch appropriations had already been approved back in September, and the 27th Amendment bars ““varying the compensation” for lawmakers until after each election.

Fox News’ Chad Pergram, Kaitlyn Schallhorn, Mike Emanuel, Matt Leach, Elizabeth Zwirz and The Associated Press contributed to this report.