IIRC we were on the other side of this with the Wall construction. The money had been appropriated and the material delivered but the POTUS was able to stop it. The argument from "our" side was that this money was already appropriated and could not be stopped. The executive has a pen and a phone.Not really all that hard, funding can be cut off easily. Congress controls the purse strings not courts. When you do things "properly" they will lose and I seriously doubt they will have the will to fight. Appropriated funding matters but performance matters as well. (Many factors but it can be done.)