Tucked into an angular lounge chair in an Art Deco suite above Radio City Music Hall on Monday evening, Ann Coulter, the conservative author, was awaiting her would-be adversary, the liberal comedian Bill Maher. She and Mr. Maher had agreed to face off in a series of debates over the next three nights, and Ms. Coulter was concerned that their material might go stale from repeated performances.

“Bill wants me to behave like a wife who laughs each time she hears her husband tell the same story,” Ms. Coulter said. “I told him I’m not an actress, or I’d have a bigger apartment.”

A few minutes later, Mr. Maher, host of the HBO series “Real Time With Bill Maher,” entered the room, dressed in jeans and a Planet Hollywood jacket. He hugged Ms. Coulter, and noted the high-heeled shoes she was wearing.

“Did you get taller?” Mr. Maher asked.

“I wanted to intimidate you,” Ms. Coulter replied teasingly. They sat as their moderator, Mark Halperin, an editor at large for Time magazine, explained the rules of the debate (“Basically, I’m going to stay out of your way,” Mr. Halperin said), then retired to separate dressing rooms.