"I can relate, and I'm sure the people who are on the receiving end will make adjustments; they always do," Trump said.
He claimed that "many of those people agree with what I'm doing" on refusing to reopen the government without obtaining funding for his long-promised border wall.
While Trump was headed to Camp David, Pence was scheduled to meet again with congressional leadership staff.
Trump, whose shifting messages during the shutdown have vexed Democrats as well as members of his own party, told reporters that he didn't "expect anything to happen" at Pence's meeting but that "we're going to have some very serious talks come [tomorrow, Wednesday, Thursday]."
Yesterday, Pence refused to budge from the more than US$5 billion Trump has demanded from Congress to pay for a portion of the wall, according to two Democratic officials briefed on the negotiations.
The standoff - which has heavily affected national parks and other operations and threatens to halt payments as varied as food stamps and tax refunds - has made Trump's unrealised border wall the linchpin of his presidency as he seeks to make good on a signature campaign promise.
House Speaker Nancy Pelosi, in her first sit-down interview on network television since reclaiming the gavel last week, maintained that the goal of yesterday's meeting was to reopen the government and blamed Trump for the continued impasse.
She also blasted Trump for suggesting that he may unilaterally move to build the border wall.
"The impression you get from the President (is) that he would like to not only close government, build a wall, but also abolish Congress so the only voice that mattered was his own," Pelosi told Jane Pauley in the interview, which aired on CBS News.
The White House is insisting that Trump is prepared to continue the shutdown fight for as long as it takes.
"Absolutely, the President means what he says when he says that," White House press secretary Sarah Sanders said on Fox News when asked about Trump's claim that he will allow the shutdown to stretch on for months or even years.
She added that it is "incomprehensible" that Democrats who agree with Trump on the need for border security would not agree to his demand for wall funding. "They just are unwilling to let this president win," Sanders said.
Trump's consideration of using emergency powers was hotly debated by those on both sides of the issue.
Mick Mulvaney, the acting White House chief of staff, defended Trump on CNN, arguing that the President has "a great deal of latitude over how the government is run".
"Presidents have authority to defend the nation," Mulvaney said. "The President has asked every single Cabinet secretary and the Office of Management and Budget to go out and find money that can be used legally to guard the southern border, which is exactly what we're going to do."
House Armed Services Committee Chairman Adam Smith said that while Trump may have the power to act unilaterally, doing so is likely to open him up to legal challenges.
"There is a provision in law that says the President can declare an emergency. It's been done a number of times. But primarily it's been done to build facilities in Afghanistan and Iraq," Smith said on ABC. "In this case, I think the President would be wide open to a court challenge saying, 'Where is the emergency?' You have to establish that in order to do this."
But House Intelligence Committee Chairman Adam Schiff said Trump's words were just "threatening talk" with no power behind them.
After bowing to his base and refusing to compromise with Democrats, Schiff said, Trump needs to "figure out how he unpaints himself from that corner".
"Look, if Harry Truman couldn't nationalise the steel industry during war-time, this president doesn't have the power to declare an emergency and build a multibillion-dollar wall on the border. So, that's a non-starter," the Democrat said.
