What happens if no criminal lawyer is willing to represent you in court?

Okay, let’s say. A person, kills a 1000 children. all 1-15 years old. Horrible crime. There’s not exactly proof, but strong evidence shows the person did do the crime. Now, lets say no Private attorney wants to defend him. and All the appointed lawyers refuse, and would rather leave there job because he is such an awful person. Could the Judge be the lawyer at that point, and make the discussion.