Trump's first Oval Office speech will be followed by a Thursday visit to the southern border to highlight his demand for a barrier. White House press secretary Sarah Huckabee Sanders tweeted that he will "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 again Tuesday that the idea of making such a declaration remains on the table.
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.
"The passion you hear from President Trump, his determination to take this case to the American people, as he will tonight in his national broadcast from the Oval Office, comes from this president's deep desire to do his job to protect the American people," Pence said Tuesday on ABC's "Good Morning America."
"We're going to continue to carry that case forward until the Democrats in Congress come to the table and start negotiating, not just to end the government shutdown but to address what is an undeniable crisis at our southern border," added Pence who also lobbied for Trump during appearances on CBS and NBC.
House Speaker Nancy Pelosi and Senate Democratic leader Chuck Schumer have come to the White House for several negotiating rounds with Trump. Democratic congressional staffers also participated in weekend talks led by Pence at the White House.
Pelosi and Schumer called for equal time to respond to Trump.
"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 said in a joint statement 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, now in its 18th day, is the second-longest in history and would become the longest this weekend.
Leaders of the nonpartisan National Governors Association made public a letter Tuesday sent to Trump and congressional leaders a day earlier, calling on them to reopen the government, saying "shutdown should not be a negotiating tactic as disagreements are resolved."
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 to reopen federal agencies, starting with the Treasury Department to ensure Americans receive their tax refunds.
In a pre-emptive move, the White House said Monday that tax refunds would be paid despite the shutdown. That shutdown exemption would break from past practice 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 the administration is working to contain the fallout 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, remove 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 U.S. airport security acknowledged an increase in the number of employees missing work or calling in sick.
But Trump and the Transportation Security Administration pushed back on any suggestion that the call-outs represented a "sickout" that was having a significant effect on U.S. air travel. Over the weekend, travelers reported longer checkpoint lines at some airports, including LaGuardia in New York.
TSA said the effect was "minimal" and that it screened more than 2.2 million passengers Sunday, a historically busy day due to holiday travel. Ninety percent waited less than 15 minutes, the agency said.
Talks over ending the shutdown have been at an impasse over Trump's demand for the wall. He has offered to build it using 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 what it's made of. 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.
Trump has tasked Pence to negotiate with Democrats, including during weekend talks. He is also 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 at a briefing Monday that, "We've been in touch with those members and others."
He said he and Homeland Security Secretary Kirstjen Nielsen would brief lawmakers at the Capitol on Tuesday and Wednesday.
Among Republicans expressing concern was Sen. Susan Collins, R-Maine, who has said Senate Majority Leader Mitch McConnell, R-Ky., should take up funding bills from the Democrat-led House. But McConnell has said he won't ask members to vote on bills that Trump won't sign.
Adding to concerns of lawmakers, federal workers still on the job apparently will miss this week's paychecks. Acting White House chief of staff Mick Mulvaney said over the weekend that if the shutdown continues into Tuesday "then payroll will not go out as originally planned on Friday night."
Trump asserted that he can 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, said he's nearly depleted his savings working without pay for the past two weeks.
"The bills don't go away," he said. "We're expected to meet our financial obligations, and we're being put in a position to not be able to meet those obligations."