The two sides traded their accusations ahead of Christmas, the fourth day in which parts of the government are closed because Congress and Trump have not been able to agree on necessary spending legislation.

On Monday, Trump asserted Democrats "must end" the standoff while Democratic leaders in Congress blamed Trump for "plunging the country into chaos."

Trump claimed the hundreds of thousands of federal workers who are furloughed due to the shutdown also want the wall, despite a lack of evidence supporting the contention.

"I can't tell you when the government is going to be open. I can tell you it's not going to be open until we have a wall, a fence, whatever they'd like to call it," Trump said in the Oval Office after a video conference with U.S. troops, who are stationed overseas.

The partial shutdown of the U.S. government has moved no closer to a resolution, with President Donald Trump asserting on Tuesday the shutdown will continue until his demand for funds to construct a U.S.-Mexico border wall are met.

While government agencies dealing with national security and public safety remain open, other offices are closed and 800,000 federal workers are on furlough. Those who are considered to be essential employees are reporting for duty, but will not get a paycheck for that work until the shutdown is over.

"The president wanted the shutdown, but seems not to know how to get himself out of it," Senator Minority Leader Chuck Schumer and incoming House speaker Nancy Pelosi wrote in a joint statement. "The stock market is tanking and the president is waging a personal war on the Federal Reserve after he just fired the secretary of defense," they said.

Trump has demanded $5 billion for a wall along the U.S.-Mexico border. Democrats have offered $1.3 billion for other border security measures. The president canceled his Christmas vacation to his Florida resort because of the impasse with Congress. "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 Monday. "At some point, the Democrats not wanting to make a deal will cost our Country more than the Border Wall we are all talking about. Crazy."

Another Trump tweet claimed "virtually every Democrat" strongly supported a "Border Wall or Fence" but turned against the idea after he made it an important part of his campaign for president.

"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! -- Donald J. Trump (@realDonaldTrump) December 24, 2018."

Most Republican lawmakers, meanwhile, have rallied around Trump's demand. "One would think that securing our homeland, controlling our borders and protecting the American people, would be bipartisan priorities... a core duty of any nation's government," Republican Senate Majority Leader Mitch McConnell said.

In the past, Democrats have been open to approving additional border security funding, including money for a wall, as part of a larger deal on immigration reform. Earlier this year, Democrats were willing to support wall funding in return for protections for so-called "Dreamers" -- immigrants brought to America illegally as children -- a deal Trump initially hailed but later abandoned.

Democrats say Trump was willing to sign a deal to keep the government operating without the full $5 billion, but backed out after those Schumer calls and "right-wing radio and TV talk show hosts" complained. "Different people from the same White House are saying different things about what the president would accept or not accept... making it impossible to know where they stand at any given moment," Schumer and Pelosi said.

What is certain, though, is the government will remain closed at least through Thursday and, according to acting Chief of Staff Nick Mulvaney, quite possibly into 2019.