With no breakthrough in sight, President Donald Trump will argue his case to the nation on Tuesday night that a 'crisis' at the US-Mexico border requires the long and invulnerable wall he's demanding before ending the partial government shutdown.

Hundreds of thousands of federal workers face missed paychecks on Friday as the shutdown drags through a third week.

Trump's Oval Office speech — his first as President — will be followed by his visit on Thursday to the southern border to highlight his demand for a barrier. White House press secretary Sarah Huckabee Sanders tweeted that he will use the visit to 'meet with those on the front lines of the national security and humanitarian crisis'.

The administration is also at least talking about the idea of declaring a national emergency to allow Trump to move forward on the wall without Congress approving the $5.6 billion he wants. Vice-President Mike Pence said the White House counsel's office is looking at the idea. Such a move would certainly draw legal challenges, and Trump — who told lawmakers he would be willing to keep the government closed for months or even years — has said he would like to continue negotiations for now.

Trump's prime-time address will be carried live by ABC, CBS, CNN, Fox Broadcasting, Fox News Channel, Fox Business Network, MSNBC and NBC.

House Speaker Nancy Pelosi and top Senate Democrat Chuck Schumer called on the networks to give Democrats a chance to respond. 'Now that the television networks have decided to air the President's address, which if his past statements are any indication will be full of malice and misinformation, Democrats must immediately be given equal airtime,' they wrote in a joint statement released on Monday night.

As Trump's speech and border visit were announced, newly empowered House Democrats — and at least a few Republican senators — stepped up pressure on GOP lawmakers to reopen the government without giving in to the President's demands. The closure, which has lasted 17 days, is already the second-longest in history and would become the longest this weekend.

Leaning on Senate Republicans, some of whom are growing anxious about the impact of the shutdown, Pelosi said the House would begin passing individual bills this week that would reopen federal agencies, starting with the Treasury Department to ensure Americans receive their tax refunds.

The White House moved to pre-empt the Democrats, telling reporters on Monday that tax refunds would be paid despite the shutdown. That shutdown exemption would break from the practice of earlier administrations and could be challenged.

'There is an indefinite appropriation to pay tax refunds. As a result ... the refunds will go out as normal,' said Russell Vought, acting director of the White House budget office.

There were other signs that administration was working to control the damage from the shutdown, which has furloughed 380,000 federal workers and forced another 420,000 to work without pay. The National Park Service said it was dipping into entrance fees to pay for staffing at some highly visited parks to maintain restrooms, clean up trash and patrol the grounds, after reports of human waste and garbage overflowing in some spots.

Over the weekend, the federal agency tasked with guaranteeing US airport security acknowledged an increase in the number of its employees missing work or calling in sick.

But Trump and the Transportation Security Administration pushed back on any suggestion that the call-outs at the agency represented a 'sickout' that was having a significant effect on US air travel. TSA said it screened more than 2.2 million passengers Sunday, a historically busy day due to holiday travel. Ninety per cent waited less than 15 minutes, the agency said.

'We are grateful to the more than 51,000 agents across the country who remain focused on the mission and are respectful to the traveling public,' said TSA spokesperson Michael Bilello.

A boy looks at the border wall, topped with razor wire and bathed in floodlights from the US side, as he walks on the beach on Monday in Tijuana, Mexico. AP

The talks over ending the shutdown have been at an impasse over Trump's demand for the wall. He has offered to build the barrier with steel rather than concrete, billing that as a concession to Democrats' objections. They 'don't like concrete, so we'll give them steel', he said.

But Democrats have made clear that they object to the wall itself, not how it's constructed. They see it as immoral and ineffective and prefer other types of border security funded at already agreed-upon levels.

'Maybe he thinks he can bully us. But I'm from Brooklyn. You let a bully succeed, you'll be bullied again worse,' Schumer said at a breakfast with the Association for a Better New York.

At the White House, spokesperson Mercedes Schlapp complained that Democratic leaders have yet to define what they mean when they say they are for enhancing border security.

'Democrats want to secure the border? Great. Come to the table,' she said on Monday. 'We are willing to come to a deal to reopen the government.'

Trump has tasked Pence during the shutdown fight to negotiate with Democrats, including during talks over the weekend with Democratic staffers. But the vice-president is increasingly being called upon to prevent defections in the GOP ranks.

Asked whether cracks were forming between the White House and Republicans eager for the shutdown to end, Pence told reporters, 'We've been in touch with those members and others.'

He said that he and Homeland Security Secretary Kirstjen Nielsen would be at the Capitol on Tuesday and Wednesday to brief lawmakers.

Among the Republicans expressing concern was Sen. Susan Collins, R-Maine, who said Senate Majority Leader Mitch McConnell should take up funding bills from the Democrat-led House.

'Let's get those reopened while the negotiations continue,' Collins said Sunday on NBC's Meet the Press.

However, McConnell has said he won't take up funding bills without Trump's support.

Adding to concerns of lawmakers, federal workers who are still on the job apparently will miss this week's paychecks. Acting chief of staff Mick Mulvaney said on NBC's Meet the Press that if the shutdown continues into Tuesday, 'then payroll will not go out as originally planned on Friday night'.

Trump asserted that he could relate to the plight of the federal workers who aren't getting paid, though he acknowledged they will have to 'make adjustments' to deal with the shutdown shortfall.

Not so easy, many of them say.

Derrick Padilla, a corrections officer with the Federal Bureau of Prisons in Colorado, has worked without pay for two weeks and said he's nearly depleted his savings.

'It's now becoming a game of, 'OK, who's going to get paid? How am I going to make this payment? What's the most important thing I have to pay for this month?'' he said.

'The bills don't go away,' Padilla added. 'We're expected to meet our financial obligations, and we're being put in a position to not be able to meet those obligations.'

For furloughed federal workers in Washington, some at least could enjoy the prospect of baseball in a few months. The Washington Nationals said season ticket holders who are laid off or not being paid by the federal government could postpone monthly ticket payments until the government is back up and running.