“Name the delegated power for a federal shut down...”
I assume it comes under the umbrella term “emergency powers” which were delegated to the president by acts of Congress, which power was delegated to the Congress by the Constitution. The same powers of delegation that allows the president to carry around the nuclear football, a power not delegated directly to the president by the Constitution.
Congress has the enumerated power to grant to others powers it does not itself possess?
The nuclear football is a bad example, for Congress does indeed have a specific enumerated Power to set rules for the armed forces, and our biggest munitions are possessed by same.