"I often said during rallies, with little variation, that 'Mexico will pay for the Wall, '" he tweeted.
House Speaker Nancy Pelosi and Senate Democratic leader Chuck Schumer forcefully rebutted the President in a speech of their own Tuesday where Pelosi accused Trump of "holding the American people hostage" to his demands.
The pressure on Washington to strike a deal intensified Friday when most workers missed their paychecks for the first time. Trump, they argue, could tell backers that he was doing all he could to fight for the wall, even if his order were held up or blocked in court.
A congressional official said the White House has directed the Army Corps of Engineers to look for billions of dollars earmarked a year ago for disaster response for Puerto Rico and other areas that could be diverted to a border wall as part of the emergency declaration.
As the shutdown has dragged on, the President has increasingly talked about the possibility of declaring a national emergency in an effort to secure border funding, a move that would be expected to face legal challenge if it happened.
Todd Semonite, commanding general of the Army Corps of Engineers, was traveling with Trump on Thursday.
A second official with knowledge of the proposal said it would fund construction of about 315 miles (500 kilometers) of border barrier.
Trump visited McAllen, Texas, and the Rio Grande on Thursday to highlight what he calls a crisis of drugs and crime along the border. The White House has directed the Corps to review its budget, including $13.9 billion in emergency funds earmarked past year by Congress, to see what money could be diverted to building a wall. Trump said Thursday that his lawyers have told him he has the "absolute right".
Rep. Patrick McHenry of North Carolina, the top Republican on the Financial Services Committee, said Wednesday's vote was "a political stunt", as the House had already passed a single appropriations package seeking to open all of the departments of the government. "It would be an incredible disservice to the American people and the economy" to divert the money to the border wall, he said.
The Independent San Juan Mayor Carmen Yulin Cruz has been critical of President Donald Trump's response to disasters in Puerto Rico.