Three confidants of President Donald Trump, including his departing chief of staff, are indicating that the president's signature campaign pledge to build a wall along the United States-Mexico border would not be fulfilled as advertised.

Trump sparked fervent chants of "Build that wall!" at rallies before and after his election and more recently cited a lack of funding for a border wall as the reason for partially shutting down the government. At times the president has also waved off the idea that the wall could be any kind of barrier.

However, White House chief of staff John Kelly told the Los Angeles Times in an interview published on Sunday that Trump abandoned the notion of "a solid concrete wall early on in the administration".

"To be honest, it's not a wall," Kelly said, adding that the mix of technological enhancements and "steel slat" barriers the president now wants along the border resulted from conversations with law enforcement professionals.

Along the same lines, White House counselor Kellyanne Conway called discussion of the apparent contradiction "a silly semantic argument".

"There may be a wall in some places, there may be steel slats, there may be technological enhancements," Conway told Fox News Sunday.

"But only saying 'wall or no wall' is being very disingenuous and turning a complete blind eye to what is a crisis at the border."

Sen. Lindsey Graham, the South Carolina Republican who is close to the president, emerged from a Sunday lunch at the White House to tell reporters that "the wall has become a metaphor for border security" and referred to "a physical barrier along the border".

Graham said Trump was "open-minded" about a broader immigration agreement, saying the budget impasse presented an opportunity to address issues beyond the border wall.

But a previous attempt to reach a compromise that addressed the status of "Dreamers" young immigrants brought to the US as children broke down last year as a result of escalating White House demands.

Graham said he hoped to end the shutdown by offering Democrats incentives to get them to vote for wall funding and told CNN before his lunch with Trump that "there will never be a deal without wall funding".

Graham proposed to help two groups of immigrants get approval to continue living in the US: about 700,000 young "Dreamers" brought into the US illegally as children and about 400,000 people receiving temporary protected status because they are from countries struggling with natural disasters or armed conflicts. He also said the compromise should include changes in federal law to discourage people from trying to enter the US illegally.

"Democrats have a chance here to work with me and others, including the president, to bring legal status to people who have very uncertain lives," Graham said.

The partial government shutdown began on December 22 after Trump bowed to conservative demands that he fight to make good on his vow and secure funding for the wall before Republicans lose control of the House on Wednesday.

Democrats have remained committed to blocking the president's priority, and with neither side engaging in substantive negotiation, the effect of the partial shutdown was set to spread and to extend into the new year.

In August 2015 during his presidential campaign, Trump made his expectations for the border explicitly clear, as he parried criticism from rival Jeb Bush, the former Florida governor.

"Jeb Bush just talked about my border proposal to build a 'fence'," he tweeted.

"It's not a fence, Jeb, it's a WALL, and there's a BIG difference!"

Trump suggested as much again in a tweet on Sunday: "President and Mrs Obama built/has a ten foot Wall around their DC mansion/compound. I agree, totally necessary for their safety and security. The US needs the same thing, slightly larger version!"

Aside from what constitutes a wall, neither side appeared ready to budge off its negotiating position. The two sides have had little direct contact during the stalemate, and Trump did not ask Republicans, who hold a monopoly on power in Washington until Thursday, to keep Congress in session.

Talks have been at a stalemate for more than a week, after Democrats said the White House offered to accept $2.5 billion for border security.

Senate Democratic leader Chuck Schumer told Vice President Mike Pence that it wasn't acceptable, nor was it guaranteed that Trump, under intense pressure from his conservative base to fulfill his signature campaign promise, would settle for that amount.

Conway claimed on Sunday that "the president has already compromised" by dropping his request for the wall from $25 billion, and she called on Democrats to return to the negotiating table.

"It is with them," she said, explaining why Trump was not reaching out to Democrats.

Democrats maintain that they have already presented the White House with three options to end the shutdown, none of which fund the wall, and insist that it's Trump's move.

"At this point, it's clear the White House doesn't know what they want when it comes to border security," said Justin Goodman, Schumer's spokesman.

"While one White House official says they're willing to compromise, another says the president is holding firm at no less than $5 billion for the wall. Meanwhile, the president tweets blaming everyone but himself for a shutdown he called for more than 25 times."

After canceling a vacation to his private Florida club, Trump spent the weekend at the White House.

He has remained out of the public eye since returning early on Thursday from a 29-hour trip to visit US troops in Iraq, instead taking to Twitter to attack Democrats. He also moved to defend himself from criticism that he couldn't deliver on the wall while the GOP controlled both the House and Senate.

"For those that naively ask why didn't the Republicans get approval to build the Wall over the last year, it is because IN THE SENATE WE NEED 10 DEMOCRAT VOTES, and they will gives us "NONE" for Border Security!," he tweeted.

"Now we have to do it the hard way, with a Shutdown."

Democrats have vowed to pass legislation restoring the government as soon as they take control of the House on Thursday, but that won't accomplish anything unless Trump and the Republican-controlled Senate go along with it.

The shutdown has forced hundreds of thousands of federal workers and contractors to stay home or work without pay.