If Trump tries to fires Mueller, there will be an avalanche of leaks exposing the campaign and probably the President, in the Russia hacking scandal. Mueller is well regarded in the FBI and firing him would show contempt for the rule of law. 
It would cause every principled official in government law enforcement to believe it is their patriotic duty to bring down the President.
So far all we've seen is the reluctance of elected politicians to work in the best interests of the people they represent.