Lawmakers tried to reassure federal employees that Congress was aware of the financial hardship they are enduring.
Every previous shutdown has been ended with a deal to pay them anyway for work they did not do, and the Senate's bill Thursday does the same.
"I'm not going to do it so fast", Trump told the White House press pool.
In Washington, federal workers denounced Trump at a rally with congressional Democrats, demanding he reopen the government so they can get back to work.
Democrats, led by House Speaker Nancy Pelosi, D-Calif., and Senate Minority Leader Chuck Schumer, D-N.Y., have vowed to block any sort of funding for the wall, accusing the president of having "manufactured" a crisis at the border.
But not everyone in the administration is on board. "Do you take an oath to the Constitution, or do you take an oath to President Trump?"
Almost $14 billion in emergency disaster relief funds have been allocated but not yet obligated through contracts for a variety of projects in states including California, Florida and Texas and in the US territory of Puerto Rico that have been ravaged by recent hurricanes, wildfires and other natural disasters, according to the aide familiar with the matter.
Rep. Peter DeFazio, D-Ore., the incoming chairman of the Transportation and Infrastructure Committee, said in an interview that rebuilding the disaster areas is "a way higher priority benefiting the American people than a wasteful wall".
That's the same length of time as the 21-day shutdown that stretched from December 1995 to January 1996 as a result of a clash between President Bill Clinton and the GOP Congress.
He has the right to undertake a construction project of this scale in times of war and national emergency, usually by allocating funds from the department of defence.