Addressing a cabinet meeting on the 12th day of the partial shutdown, Trump warned it "could be a long time" before the impasse is resolved.
"It's too important a subject to walk away from," said the president, who was to meet later with Democratic and Republican lawmakers.
"The 5.6 billion is such a small amount and we are talking about national security," Trump added, saying: "I think the people of this country think I am right."
Trump is set to meet top Democratic lawmakers Nancy Pelosi and Chuck Schumer in a bid to break the long impasse.
It will be Trump's first meeting with Pelosi, who will take over as speaker of the House on Thursday, and Schumer, the Senate minority leader, since an acrimonious Oval Office meeting with the pair on December 11.
Democrats say the border wall, one of Trump's key campaign promises, is a distraction from more complicated immigration problems and a tool for Trump to whip up support among his conservative base.
The standoff resulted in swaths of the federal government being shut down over the Christmas and New Year holidays -- and for the foreseeable future until a deal is reached.