Pence has also stated that Trump's address would lay out the facts of what the administration has called a humanitarian and security crisis at the southern border.
They say he is using false claims and manufacturing a crisis to carry out his 2016 presidential campaign promise for a wall that he said at the time would be paid for by Mexico.
Democrats have reminded the president about his pledge and, therefore, are willing to give him only $2 billion for the border security funding. Hundreds of thousands of federal workers are going without pay, and government disruptions are hitting home with everyday Americans. Ahead of Tuesday night's speech, Trump aides went so far as to claim that 4000 suspected terrorists had been apprehended at the Southern border, forcing even he pro-administration Fox News to fact-check and say most were apprehended at airports.
The dispute over wall funding - Trump is demanding $5.7 billion USA to help build it - led to a stalemate in Congress over funding for parts of the government.
Trump's speech is set to be followed by a rebuttal from House Speaker Nancy Pelosi and Senate Minority Leader Chuck Schumer, who oppose the wall and have called on Trump to end the shutdown.
A growing proportion of Americans blame Mr Trump for the government shutdown, although Republicans mostly support his refusal to approve a budget that does not include funds for the wall, according to a Reuters/Ipsos poll released on Tuesday.
"This barrier is absolutely critical to border security".
But the president would be accused of usurping Congress's constitutional power of the purse, and the move would be bogged down in a quagmire of legal challenges.
Mr Trump deployed about 5,800 troops to the border and described the migrants as an "invasion".
Trump has long maintained that a border wall is needed to stem the flow of illegal immigration and drugs, and in recent weeks has made the issue a priority.
The number of illegal border crossings is down from 1.6 million in 2000 to fewer than 400,000 past year. Journal is reporting that Trump is looking for ways to end the shutdown without it looking like the Democrats won. Mr Trump said after recounting gruesome details of murders he said were committed by illegal immigrants.
He noted that the proposal drafted afterwards by the White House included what the other side had asked for, but said Democrats were not willing to negotiate while the government remains closed.
Trump said on January 6 he's considering declaring a national emergency as the United States struggles to stop the aliens from entering the country without permission, noting that even his opponents admit he has the authority to do so.
Some correspondents have speculated that he may ultimately resort to such a declaration as a last-ditch tactic to allow him to reopen the government without losing face to Democrats.