Ouch!!! What a dilemma!
First off, if I had been the subordinate and really didn't want to accept the assignment, I would have requested that we discuss this assignment privately after the meeting.
As a supervisor, I would have adjourned the meeting immediately and dismissed the rest of the team. After they had left, I would have given the employee an ultimatum: apologize in tomorrow's meeting and accept the assignment so that I could retain management control of the team, or don't come back at all.
Public insubordination cannot be tolerated if a manager is going to have any credible control of his/her team.