In fact, the stunned silence following Letterman's announcement was probably caused by the studio audience awaiting the punchline to the gag they thought Letterman was setting up.
"Leslie [Moonves], it's been great. You've been great. The network has been great. But I'm retiring," Letterman said from his desk.
"Really... This is... You actually did this?" was all Paul Schaffer said in the silence that followed. "Do I have a minute to call my accountant?"
"What this means now is that Paul and I can be married," Letterman said.
After he made his announcement, the studio audience gave Letterman a standing ovation in the Ed Sullivan Theatre.