This question quickly made me decide I don't want to work in a role where I may find myself in this position! Especially since it's unlikely I wouldn't be given authority to make sensible recommendations to changes.
I answered that I would consider and prioritise which message was of the up most importance to be shared with the public. Note: The interviewers sneered at my response...claiming that you shouldn't de-prioritise a request from a senior councillor, no matter what!
I answered that I thought the mayor was doing better than the prime minister in his role as he appears well briefed on any given subject, unphased and sincere in his response to difficult questions and does a lot more interviews off the cuff.