Here is Heritage/John Malcolm on the authority
In a recent study, the Brennan Center for Justice at the New York University School of Law identified
136 different provisions of law granting a president a range of powers he can exercise if he declares a national emergency. The powers that a president can utilize under such circumstances can be quite broad. Indeed, the Congressional Research Service has said:
Under the powers delegated by such statutes, the president may seize property, organize and control the means of production, seize commodities, assign military forces abroad, institute martial law, seize and control all transportation and communication, regulate the operation of private enterprise, restrict travel, and, in a variety of ways, control the lives of United States citizens.
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There are two other laws that the president might cite, but both come with some important caveats.
The first would apply if a president were to declare a national emergency “that requires the use of the armed forces.” If that were to happen, the secretary of defense could authorize the military departments to “undertake military construction projects … that are necessary to support such use of the armed forces” so long as the amount spent on such projects does not exceed “the total amount of funds that have been appropriated for military construction, including funds appropriated for family housing, that have not been obligated.”
The second would apply if a president were to declare a national emergency “that requires or may require the use of the armed forces.” If that were to happen, the defense secretary would be empowered to “(1) terminate or defer the construction, operation, maintenance, or repair of any Department of the Army civil works project that he deems not essential to the national defense, and (2) apply the resources of the Department of the Army’s civil works program, including funds, personnel, and equipment, to construct or assist in the construction, operation, maintenance, and repair of authorized civil works, military construction, and civil defense projects that are essential to the national defense.”
Trump Has a Strong Legal Argument That He Can Declare National Emergency at Border