In heavy 3-quart saucepan, melt butter over low heat. Stir in flour. Cook 3 minutes, stirring constantly. Stir in broth; heat to boiling. Boil 2 to 3 minutes, stirring constantly, until mixture is thick and smooth.
Reduce heat to low. Add cheese, 1 cup at a time, stirring over low heat until cheese is melted and mixture is smooth. Stir in pepper sauce. Pour cheese mixture into fondue pot; keep warm over low heat.
Spear vegetables with fondue forks. Dip and swirl vegetables in fondue.