But critics say the security risks are overblown and his administration is at least partly to blame for the humanitarian situation.
The president is insisting that $US5 billion ($NZ7.4b) be included for the border wall. The goal of the address will be to promote his planned border wall between the United States and Mexico, characterize the issue of border security as a national security crisis and convince enough Americans to change their views on the subject that Trump can end the government shutdown by receiving border wall funding.
Since the stalemate over funding is ongoing, Trump had no other choice but to take his case directly to American people in a speech planned for later in the day, the vice president said, as suspense continues to build over the possible big announcement.
Democrats have said they support increased border security measures such as additional US border agents and technology, but have rejected the administration's claims about the security risks at the border and have raised concerns that Trump will use his speech to present a false narrative.
Trump will tell the American people that there is "a humanitarian and security crisis" at the border, Pence said in television interviews on Tuesday morning.
While its repercussions ripple across the country, Mr Trump has also threatened to bypass Congress and invoke emergency powers to build the wall along half the 2,000-mile (3,100km) border. "Tuesday night at 9:00 P.M. Eastern".
Some two dozen Republicans are expected to cross over this week and vote for the Democratic bills to re-open government, said a GOP aide who was not authorized to speak publicly. He asserted that the government remained shut down because Democrats wouldn't fund border security. It was just one of several measures to combat the "crisis" at the border. "It would very quickly pay for itself". "The cost of illegal drugs exceeds US$500 billion a year, vastly more than the US$5.7 billion we have requested from Congress", Trump said.
Len Saunders, an immigration lawyer based near the border in Blaine, Wash., said those border guards - many of whom are supportive of the president's border-security efforts - may soon stop showing up for work as they begin to feel the shutdown's financial impact.
Mr Trump deployed about 5,800 troops to the border and described the migrants as an "invasion".
House Majority Leader Steny Hoyer said the House Democratic leadership had not yet worked out a strategy for how to respond if Trump declared a national emergency in to circumvent Congress and build the wall.
During the campaigning he pledged Mexico would pay for the wall, but since taking office he has been unable to achieve this, and is now attempting to use United States taxpayer funds to the tune of US$5.7 billion (NZ$8.5b).
"The president was asked whether it [the national emergency option] is something he was considering, and he said it is something we are looking at...."
US President Donald Trump wants the Democrats to approve funding for a wall to end a government shutdown.