Sources within the Democratic party familiar with the matter told AP on condition of anonymity that the White House offered $2.5 billion, with an initial $2.1 billion plus $400 million - in what Democrats have called a "slush fund" - for the president's other immigration priorities.
"I'll call it whatever they want, but it's all the same thing", he told reporters after participating in a holiday video conference with representatives from the five branches of the USA military stationed in Alaska, Bahrain, Guam and Qatar.
Trump claimed that many of these workers "have said to me and communicated, 'stay out until you get the funding for the wall.' These federal workers want the wall".
Trump followed up on a Monday tweet in which he said he "just gave out a 115 mile long contract for another large section of the Wall in Texas".
Trump said Tuesday that the wall as he envisions it would be a fortress that no normal human could breach.
The downturn has caused great uncertainty in the White House as Trump has sought someone to blame, and he has lashed out publicly at Powell. "So, if we can do that, without the wall, I think that's a solution".
Mr Trump argued that Democrats oppose a wall only because he is for one.
The border wall was one of Trump's signature campaign promises, which he said is necessary to ensure border security, and prevent unvetted people from coming across illegally.
"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.
On Monday, Trump asserted Democrats "must end" the standoff while Democratic leaders in Congress blamed Trump for "plunging the country into chaos".
In a sign the president's strategy has sparked serious unease among Republicans, Senator Pat Roberts of Kansas - the only senator at the Capitol Monday - suggested a compromise to reopen the government but without wall funding.
It's no secret what Donald Trump wants for Christmas, and there's nothing Santa can do about it. "Congress and the White House have not done their fundamental jobs of keeping the government open".
Both sides seem entrenched in their opposing stances and it's possible parts of the government could remain closed until the new Congress is seated in the first week of January, when Democrats will take control of the House. The negotiations have centred on border security funding amounts and how that spending would be restricted.
"We moved off of the five and we hope they move up from their 1.3", Mulvaney said less than a day after a senior administration official insisted that Congress would have to cave into Trump's demand for the shutdown to end, highlighting Trump's unpredictable negotiating style.
Trump criticized the Federal Reserve on Monday, describing it as the "only problem" for the United States economy, even as top officials convened the "plunge protection team" forged after the 1987 crash to discuss the growing rout in stock markets. "It doesn't have to be a 30-foot tall concrete" barrier, he said.