Still, the administration might argue that Congress has effectively preapproved a wall-like barrier under other laws, including one that authorizes the military to construct border “fences” blocking drug-smuggling corridors, and another, the Secure Fence Act of 2006, that empowers the Department of Homeland Security to build “physical infrastructure enhancements” along the border.

The government could skip the requirement to identify pre-existing authorization for a wall if it invoked a different emergency-powers law for the funds, but that route would raise other problems, Ms. Goitein said. Among them, the government would need to show that a wall meets the legal definition of military construction even though it is not clearly tied to a military facility or installation and that the southern border situation represents the kind of emergency that requires the use of the armed forces.

Does it matter if there is no true emergency?

Probably not.

If Mr. Trump declares that the situation along the southern border suddenly constitutes an emergency that justifies building a wall without explicit congressional sanction, he will run up against a reality: that the facts on the ground have not drastically shifted. The number of people crossing the border unlawfully is far down from its peak of nearly two decades ago. The recent caravans from Central America primarily consist of migrants who are not trying to sneak across the border but instead are presenting themselves to border officials and requesting asylum.

And while Mr. Trump and his aides keep claiming that terrorists are sneaking in across the border, including assertions that they are doing so by the thousands, as a matter of empirical reality, there has been no such instance in the modern era.

Still, as a matter of legal procedure, facts may be irrelevant. Before a court could decide that Mr. Trump had cynically declared an emergency under false pretenses, the court would first have to decide that the law permits judges to substitute their own thinking for the president’s in such a matter. The Justice Department would surely argue that courts should instead defer to the president’s determination.

“If any court would actually let itself review whether this is a national emergency, he would be in big trouble,” Ms. Goitein said. “I think it would be an abuse of power to declare an emergency where none exists. The problem is that Congress has enabled that abuse of power by putting virtually no limits on the president’s ability to declare an emergency.”

Why did Congress give presidents such broad power?

In part by accident. When passing many emergency-powers laws, Congress attached a procedure that would let lawmakers override any particular invocation of that authority. The National Emergencies Act, for example, permitted Congress to rescind an emergency if both the House and the Senate voted for a resolution rejecting the president’s determination that one existed.

But in 1983, the Supreme Court struck down such legislative vetoes. The justices ruled that for a congressional act to have legal effect, it must be presented to the president for signature or veto. Because it takes two-thirds of both chambers to override a veto, the ruling significantly eroded the check and balance against abuse that lawmakers had intended to be part of their delegation of standby emergency powers to presidents.