Meanwhile, US television networks, which agreed to Trump's request for a prime-time telecast of his speech after some deliberation, have also consented to air Democrats' response to the address after a fervid debate on whether the President would get away with lies and disinformation.
Democrats have said they support increased border security measures such as additional U.S. border agents and technology, but have rejected the administration's claims about the security risks at the border and have raised concerns that Mr Trump will use his speech to present a false narrative.
The president is insisting that $US5 billion ($NZ7.4b) be included for the border wall.
Large chunks of the government were shut down on December 22 after politicians and the President hit an impasse over Mr Trump's demands to build a wall.
White House press secretary Sarah Huckabee Sanders said in a tweet that Mr Trump would use his visit to the border on Thursday to "meet with those on the front lines of the national security and humanitarian crisis".
'There is a humanitarian and national security crisis, ' Vice President Mike Pence told reporters Monday amid concerns Trump would declare a national emergency that would empower him to construct the $5.6 billion border wall without congressional approval.
Invasion of the jellyfish: 13,000 beach goers stung in just one week
Surf Life Saving Queensland said on Saturday a "wall of bluebottles" was approaching Rainbow Beach, prompting a closure. About 13,000 stings were recorded in the past week - three times more than in the corresponding period previous year .
Democrats have repeatedly slammed the proposed wall but have remained vague about counter-proposals that would curb illegal immigration.
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.
The number of illegal border crossings is down from 1.6 million in 2000 to less than 400,000 previous year.
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.
In a pre-emptive move, the White House said Monday that tax refunds would be paid despite the shutdown.
It also found that only 35 percent of adults in the United States support a congressional spending bill that includes funding for the wall, and 25 percent support Trump's decision to keep the government closed until Congress approves funding for the wall. The shutdown, which has left some 800,000 government workers furloughed or working without pay, is also affecting national parks, airline security screening, housing and food aid, and economic data. But mostly Trump still wants his wall, which Democrats describe as immoral as well as no solution to illegal immigration. While Trump has previously described the situation on the border that way - including when he directed active duty troops there ahead of the midterm elections- he has never signed an official proclamation.
Trump made his promise for a wall a signature issue in his 2016 White House run.