Though both sides have moved on the money, they aren't budging on the wall. The White House insisted Trump will reject any deal that does not include money for a wall or fence; Democrats held firm in their opposition to a wall or other physical barrier.
"Nothing new. Nothing new on the shutdown. Nothing new. Except we need border security," Trump told reporters at the White House as he answered telephone calls from children who want to know when Santa will get to their homes.
In a joint statement, the Democratic leaders of Congress, Sen. Chuck Schumer and Rep. Nancy Pelosi, said that as long as Trump keeps listening to the House Freedom Caucus and others on the right flank, there is no easy resolution to the impasse.
"It's Christmas Eve and President Trump is plunging the country into chaos," they said, pointing to problems beyond the shutdown, including the plunging stock market and the president's firing of his defense secretary. "The president wanted the shutdown, but he seems not to know how to get himself out of it."
The White House presented a counteroffer over the weekend to Schumer, budget director Mick Mulvaney said Sunday. Mulvaney would only say the offer was between Trump's $5.7 billion request and $1.3 billion Democrats have offered.
A Democratic aide granted anonymity to discuss the private talks confirmed the White House offered $2.5 billion - an initial $2.1 billion plus $400 million Democrats called a "slush fund" for the president's other immigration priorities.
Mulvaney said he was awaiting a response from Schumer. Schumer's office said the parties remained "very far apart."
Trump chimed in from the White House, where he has been cooped up since the shutdown began early Saturday.
"I am all alone (poor me) in the White House waiting for the Democrats to come back and make a deal on desperately needed Border Security," he tweeted. "At some point the Democrats not wanting to make a deal will cost our Country more money than the Border Wall we are all talking about. Crazy!"
Trump put off plans to head to his Florida estate for Christmas. His wife, first lady Melania Trump, returned from Florida to spend the holiday with him.
The president's border security meeting Monday afternoon included Homeland Security Secretary Kirstjen Nielsen and other department officials, White House press secretary Sarah Huckabee Sanders said.
Senate negotiators continued talks behind the scenes with Democrats and Republicans. The House and Senate briefly gaveled into session on Christmas Eve before closing again with no further action.
In their statement, Pelosi and Schumer said "different people from the same White House are saying different things about what the president would accept or not accept to end his Trump Shutdown, making it impossible to know where they stand at any given moment."
Trump blamed Democrats for the stalemate, tweeting Monday that "Virtually every Democrat we are dealing with today strongly supported a Border Wall or Fence. It was only when I made it an important part of my campaign, because people and drugs were pouring into our Country unchecked, that they turned against it. Desperately needed!"
However, an AP Fact Check found that U.S. arrests on the Mexican border jumped 78 percent in November from a year earlier to the highest level in Trump's presidency. Increased arrests indicate that more people are trying to cross the border illegally.
Several Cabinet departments and agencies have been closed since Saturday after their funding lapsed. Hundreds of thousands of federal workers across the country were affected by the closure, which expected to last at least through Thursday, when the House and Senate meet again.
Mulvaney predicted the shutdown could stretch into January, when Democrats are set to control the House.
Trump excused federal employees from work on Monday and Christmas is a federal holiday, meaning Wednesday is the first day the public could begin to feel the effects of lost government services, Mulvaney said.
The routines of about 800,000 federal employees, meanwhile, were about to be disrupted.
More than half of those employees deemed essential, including U.S. Secret Service agents and Transportation Security Administration agents, must work without pay, though retroactive pay is expected. Another 380,000 were to be furloughed, meaning they will not report to work but would also be paid later. Legislation ensuring workers receive back pay was expected to clear Congress.
Trump promised during the campaign to build a border wall and make Mexico to pay for it. Mexico has refused.
Progress toward funding the wall has been slow and Trump sees the final days of the GOP's complete control of Congress as his last chance to force the issue. But some Republicans also oppose building a wall.