Mr. Giuliani spent that morning rushing between studios — he appeared on all five major networks — pausing long enough to strike a penitential chord and write off Mr. Trump’s words as unfortunate locker-room talk.

Considering the circumstances, the campaign staff believed Mr. Giuliani had blunted the political blow Mr. Trump had inflicted on Mr. Trump. “Most people thought he did a great job,” Mr. Bossie said.

When Mr. Giuliani boarded the plane, spent from his labors, he strode down the aisle a conquering hero, swapping high-fives. Then he settled across from Mr. Trump.

Everyone could hear what the candidate said next.

“Man, Rudy,” Mr. Trump said, “you sucked. You were weak. Low-energy.”

Mr. Giuliani slumped in his seat, one witness said. The plane grew silent.

By day’s end, Mr. Giuliani was back in front of the cameras, claiming victory for Mr. Trump in the debate. And his most important work for the campaign was yet to come.