A stronger argument against Trump’s declaration is that it does not require use of the armed forces. The president is likely to argue that he must use armed forces or else the problems he seeks to resolve with his declaration will continue, and so the use of military personnel is required. This question is likely to be a close call legally, and it’s hard to predict how judges will respond.
Other critics claim the Military Construction Codification Act violates the Constitution’s nondelegation doctrine, which prohibits Congress from delegating away its legislative power to the president. I strongly support the nondelegation doctrine, see my amicus brief in the pending Supreme Court case Gundy v. United States, but the statute invoked by the president does not violate that doctrine because the nondelegation doctrine only applies to rules of private conduct. As Justice Clarence Thomas, the strongest supporter of the nondelegation doctrine on the court, recognized in DOT v. Association of American Railroads (2014), “The core of the legislative power that the Framers sought to protect from consolidation with the executive is the power to make ‘law’ in the Blackstonian sense of generally applicable rules of private conduct.”
Discretion given to the president over how the executive branch is run, or how appropriated money is spent, is merely allowing the head of the executive to exercise his default control over his subordinates.