I doubt if that would be using much CPU. I think the exception you are referring to is when the publisher finds a publishing queue for a website that has no "target" website specified. Arguably it shouldn't really log the exception - it's a warning more than anything.
If you are still experiencing this problem then it might be interesting to see a few thread dumps of the system while in this state. Three thread dumps taken at an interval of about 5 seconds should be sufficient.