The administration may seek to couple that statute with separate laws to claim Congress has already authorized various border barriers.

Still, none of those laws are a perfect fit, specialists say, raising technical disputes that will give litigants plenty to argue about in court. But a more fundamental question for what kind of historical precedent Mr. Trump’s move establishes is whether courts will even allow themselves to address whether it is true, as a matter of fact, that a national emergency exists on the border that a wall would resolve.

Critics note that the number of people crossing the border illegally is far lower than it was a generation ago. The relatively new phenomenon of caravans of migrants consists largely of families who present themselves to border officials and request asylum, rather than trying to go deeper into the interior on their own. Most illegal drugs are smuggled in through ports of entry. And there has been no instance in the modern era of a terrorist attack on domestic soil that was committed by someone who sneaked in across the southern border with Mexico.

Still, the Justice Department would surely argue that courts should not even consider the facts, but instead should defer to the president’s determination that an emergency exists. There is a long history of courts being reluctant to substitute their own thinking for the president’s in security matters — or declaring that it is a “political question” for the two politically elected branches to work out between themselves.

Congress enacted the main umbrella law that has governed how and when presidents may invoke emergency power statutes, the National Emergencies Act of 1976, during the era of post-Watergate overhaul.

At the time, while bestowing broad discretion on presidents to decide whether an emergency existed, lawmakers also created a powerful check and balance against abuse: Congress could end the declared emergency if majorities in both chambers voted for a resolution to do so. To keep a president’s partisan allies from bottling up such a measure, the law says that if one chamber passed such a resolution, the other one must bring it up for a vote within 18 days.

House Democrats have made clear they will pass such a resolution if Mr. Trump declares a border emergency, forcing Senate Republicans to take a stand on whether his move is legitimate. While Senator Mitch McConnell of Kentucky, the majority leader, said on Thursday that he would support Mr. Trump, it would take only a handful of Republican senators to break ranks for the resolution to pass anyway.