I have the Christmas lights up and have a heavy load on one circuit. The circuit breaker did not trip. However, after an hour of running the lights, the circuit breaker on the panel smells light burning ballast from a fluorescent light.

How can I determine if the circuit breaker is bad?

If you feel safe in removing the panel cover with the power still on you can test the breaker with a small tester or meter. If you put your black test lead on the black wire of the breaker and your white lead to the white neutral in the box by the buss bar you should read 110v. However, if the breaker is giving off a burnt smell I would replace it. It should pop when overloaded, not smell. If you touch the face of the breaker around the switch it is likely going to be very warm.

Wait for an answer from somebody aware that most residential service is closer to 120 volts.

If it gets warm or smells, may be loose connection on breaker, burnt or corroded buss where breaker plugs onto, or bad Breaker. Remove breaker, if qualified, look at buss, if it is burnt, new breaker on new breaker location may solve problem. New breaker on a bad buss will soon fail.