The Secret Service director, Kimberly A. Cheatle, faced bipartisan calls for her resignation on Monday, after a disastrous hourslong congressional hearing in which she declined to answer basic questions about the attempted assassination of former President Donald J. Trump.

Ms. Cheatle declined to say how many agents were protecting Mr. Trump when a gunman shot at him at a campaign rally in Butler, Pa., on July 13, or who decided to leave a nearby rooftop out of the event’s security perimeter. Nor would she tell members of the House Oversight Committee why Secret Service agents were not aware until the last seconds that people in the crowd had seen a gunman on that roof.

At times, Ms. Cheatle seemed less informed than the lawmakers quizzing her. When Representative Marjorie Taylor Greene, a Republican from Georgia, asked for a detailed timeline of events, Ms. Cheatle said she did not have one.

“I have a timeline that does not have specifics,” she said, eliciting laughter from the room.

By the hearing’s end, many of the committee’s Democrats — usually defensive of their party’s appointees — had also swung sharply against Ms. Cheatle.

Representative Jamie Raskin of Maryland, the committee’s top Democrat, said he “didn’t see any daylight between the members of the two parties today at the hearing, in terms of our bafflement and outrage.”

Mr. Raskin joined the committee’s Republican chairman, Representative James R. Comer of Kentucky, in calling for her resignation. “The director has lost the confidence of Congress, at a very urgent and tender moment in the history of the country,” Mr. Raskin said.