US Vice President Mike Pence said on Wednesday that the Trump administration was "determined to stand firm" in its push to secure more than $5bn in funding for a wall along the border with Mexico to end what he called a "humanitarian crisis".

"President Trump and I, and our entire team, are determined to stand firm until the Democrats in Congress come to the table and work with us to secure the border, build a wall, end this humanitarian crisis and do what's right for the American people," Pence said in an interview with syndicated radio show host Rush Limbaugh.

The comments come on the 19th day of a partial government shutdown, which is centred on Trump's demand for $5.7bn in funding for the wall. More than 800,000 federal workers have been furloughed or required to work without pay and services have been also disrupted for many other Americans.

On Tuesday, Trump gave a televised address in which he made the case for a border wall, saying the situation is a "humanitarian crisis - a crisis of the heart and a crisis of the soul".

Top Democrats Nancy Pelosi and Chuck Schumer responded, accusing Trump of appealing to "fear, not facts".

Democrats oppose the border wall, calling it ineffective, expensive and immoral. After taking control of the House of Representatives last week, they passed a two-bill spending package that included more than $1.3bn for border security measures that do not include a wall.

Senate Majority Leader Mitch McConnell, a Republican, has so far this year refused to bring any legislation Trump won't sign to a vote.

McConnell faces increasing pressure from within his party, especially from vulnerable Republicans up for re-election in 2020, as several conservative senators urged action to reopen the government.

Keep Republicans in line

To shore up his party's support, Trump and Pence met congressional Republicans on Wednesday for talks about the shutdown.

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Trump told reporters as he was leaving the Capitol that the party is "totally unified" in its demands for border security.

"A couple [Republicans] talked about strategy ... but they're with us all the way," he said.

But some Republicans, including Senator John Thun, have indicated in recent days that there is growing concern about the toll the shutdown is taking on everyday Americans, including disruptions in payments to farmers and trouble for home buyers who are seeking government-backed mortgage loans - "serious stuff".

Republican Senator Lisa Murkowski recently urged colleagues to approve spending bills that would reopen various agencies, "so that whether it's the Department of the Interior or it is the IRS, those folks can get back to work. I'd like to see that".

Her colleague John Cornyn called the standoff "completely unnecessary and contrived. People expect their government to work ... This obviously is not working."

Leading up to his Capitol Hill visit, Trump said he thought "we're getting closer to a deal", but presented no details on what that may be. Instead, he renewed his notice that he might declare a national emergency and try to authorise the wall on his own if Congress wouldn't approve the $5.7bn he's asking for.

"I think we might work a deal, and if we don't we might go that route," he said. If he moves forward with this threat, it will likely face challenges in the courts.

Growing proportion of Americans blame Trump: poll

As the shutdown stretched to the second-longest on record, a Reuters/Ipsos poll released on Tuesday found that a growing proportion of Americans blame Trump for the shutdown, though Republicans mostly support his refusal to approve a budget without taxpayer dollars for a wall on the US-Mexico border.

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The national opinion poll, which ran from January 1 to January 7, found that 51 percent of adults believe Trump "deserves most of the blame" for the shutdown. That is up four percentage points from a similar poll that ran from December 21 to 25.

Another 32 percent blame congressional Democrats for the shutdown and seven percent blame congressional Republicans, according to the poll. Those percentages are mostly unchanged from the previous poll.