I wouldn't be surprised if Trump just says, "military is an essential service they will be working as usual...I will be directing $5B to start for them as one of their missions to build a wall and defend National Security between us and any invading nation."
Win/Win. They can try to tie it up in court while the military builds it.
Actually, the military IS considered essential. When the shutdown happened back in the 90's for 24 days, we had to come to work, but we had to wait for the government to reopen before we got our paychecks.