On Capitol Hill, top members of both parties were trying to publicly warn the President not to follow through on his threat, arguing such a move would create a huge economic ripple across the United States.
"The economic disaster to the country would be huge," said Senate Democratic Leader Charles Schumer.
"The President is frustrated obviously," said Sen. John Thune (R-SD), the number two Republican in the U.S. Senate.
"A lot of us don't think that closing the border is a good idea, and hopefully he will come to that conclusion, too," Thune said to reporters just off the Senate floor.
A few hours later, Senate Majority Leader Mitch McConnell was more blunt, going before television cameras to warn the White House that a border shutdown would have a 'potentially catastrophic economic impact.'
In the Oval Office on Tuesday, President Trump again repeated his demand for the Congress to make a series of changes in immigration law, to end so-called 'chain migration,' get rid of what's known as the "visa lottery," and make other reforms in immigration law to allow the feds more quickly deport illegal immigrants.
But no lawmakers in positions of power are talking at all about any votes in Congress related to immigration at this time - it was just over a year ago that Mr. Trump's plans were voted on in the Senate, garnering only 39 votes, the smallest number of any immigration measure to get a vote in 2018.
"If we don't make a deal with Congress, the border is going to be closed," Mr. Trump said.