Trump noted in a tweet on Tuesday that a wall on America's southern border will pay for itself within two months.
The GOP-led House has not yet approved a Homeland Security funding bill.
Democrats, meanwhile, say the president's proposal is "wasteful" and rejected to fund the border wall.
Funding is set to expire on December 7 for some federal agencies including the Department of Homeland Security and Internal Revenue Service, which would trigger a partial shutdown unless lawmakers can navigate an impasse with Trump over spending on border security.
Congress and the White House are working on a deal for a two-week extension of government funding that would push the deadline for a fight over a possible government shutdown and money for President Trump's border wall until December 21.
Trump kept up pressure Monday on congressional Democrats funding for his promised border wall, but he also threatened other actions to deter illegal immigration as negotiations continue.
The groups argued that Trump's wall projects did not fall under that law, and that the measure was unconstitutional because it gave too much power to unelected Cabinet officials to avoid laws such as the Endangered Species Act and the National Environmental Policy Act.
But it's unclear if that would satisfy the president, who could see the chances of a border wall fade when Democrats take over the House in January.
"I would absolutely consider it and probably give it", Trump told reporters. Chuck Schumer and House Democrat Nancy Pelosi has also been delayed to next week.
The country shouldn't have to endure a shutdown over "Trump's temper tantrum", Schumer said last week.
Besides the funding bill, Congress is considering a sweeping criminal justice package with sentencing reforms, a farm bill that's a top priority of Senate Majority Leader Mitch McConnell and other items before they adjourn for the year.
During the 2016 presidential campaign, then-candidate Donald Trump attacked Curiel, who was born and raised in IN, as a "Mexican" and a "hater" incapable of impartiality in presiding over a lawsuit against Trump University.
Without action by Congress, federal agencies including the Department of Agriculture, State Department and Department of Homeland Security would find themselves without any money to pay employees and administer programs through the fiscal year that ends next September 30.
Instead of continuing the debate over money for a wall and border security, Republicans and Democrats spent the weekend negotiating the terms of an agreement that would delay the original Friday deadline.