What Trump needs to do is change the paradigm of a "shutdown." Leave the parks and monuments open. Close the EPA, Department of Labor, NLRB, Department of Education, etc. Put all those union members and bureaucrats out on their keesters but give the public the bits of government we actually want.
Clinton and the Dems designed the first "shutdown" to inflict maximum pain on the public. Let's change that and inflict max pain on the government.