A lot of businesses now rely on those clocks. Trump will be shooting himself in the foot if he goes through with this.
So the Chief Executive goes to each department and says "I want you to cut x% which we're going to use for military" and the NIST says "we can turn off WWV/WWVH/WWVB and that goes in the President's budget request to Congress.
Budget appropriations are the exclusive right of Congress.
The
Congressional Budget and Impoundment Control Act of 1974 says that if Congress allocates the money for a specific purpose, the Executive Branch will spend that money for that purpose.
I've heard rumors that WWVB will be funded in 2019.