It is a difficult hill to climb for opponents of Trump's national emergency, as the House would need two-thirds of its members to support the override of the veto.
The decision sparked criticism from Republicans and Democrats, many of whom argued that national emergency action would violate the Constitution.
The President vetoed the bill one day after his release from the Senate.
"Congress has the freedom to pass this resolution and I have a duty to veto it," Trump told the Oval Office before officially sending the measure back to Congress without his approval.
Democrats in the House, for their part, quickly announced that they would hold a vote that was canceled on March 26. "The House and the Senate categorically rejected the president's unfaithful power, while the president chose to continue defying the Constitution, the the American people," Pelosi said in a statement issued at the time.
But the House faces a major hurdle, requiring a two-thirds majority – rather than a simple majority – to override the veto. Bill 245-182 was first passed by the House. Thirteen Republicans and Democrats voted in favor of inverting the president 's state of national emergency. If all members are present for Tuesday's vote, a successful waiver would require nearly 285 votes – far less than 245.
The Democratic leaders of the House have no illusions about overreaching the veto. President Nancy Pelosi said last week that the purpose of the vote is to make clear that the new democratically controlled House will not tolerate the president's persistence in a border wall.
"It's not a question of whether we can succeed with the number of votes," Pelosi said at an event in New York. "We establish the intention of Congress."
The leader of the Senate minority, Chuck Schumer, said earlier this month that the National Emergency Act allows for a resolution of disapproval every six months and that the Democrats intend to reintroduce it. .
Phil Mattingly of CNN, Clare Foran and Ted Barrett contributed to this report.