He could start with the clerks, the most likely source of the leak, and say to them that unless someone came forward with information in the next 30 minutes, they would all be fired, effective 31 minutes from now. He won’t, of course, because that would be a demonstration of clarity and fortitude so far absent in the Court, and probably result in his being shunned by a certain group of people in DC.
Ethics Alarms 
He could start with the clerks, the most likely source of the leak, and say to them that unless someone came forward with information in the next 30 minutes, they would all be fired, effective 31 minutes from now. He won’t, of course, because that would be a demonstration of clarity and fortitude so far absent in the Court, and probably result in his being shunned by a certain group of people in DC.