Ms. Pelosi’s decision to withhold the articles of impeachment in an unsuccessful effort to extract assurances from Senate leadership about the terms of the trial has delayed the appointment of the so-called impeachment managers, raising the stakes and compressing the timetable of their already challenging task.

It is a job that veterans say is fraught with legal complexity, political pressure and historic significance.

“I really don’t want to give them any advice,” Mr. Sensenbrenner said in an interview. “But I guess I can say is that this is going to be a lot more work than you think.”

“The American people,” he added, “are going to be watching.”

The pivotal role of the managers is one reason that Ms. Pelosi has waited to send the charges to the Senate. Senator Mitch McConnell, Republican of Kentucky and the majority leader, said this week that he had the votes to move forward with an impeachment trial without committing to calling witnesses or hearing new evidence. Without knowing whether there will be witnesses to question or new complex documents to digest, the speaker cannot decide what kind of lawmakers are best suited to the task.

People close to Ms. Pelosi say it is all but certain that one of the managers will be Representative Adam B. Schiff of California, a former federal prosecutor who oversees the Intelligence Committee and led the investigation into Mr. Trump’s dealings with Ukraine. Representative Jerrold Nadler of New York, the chairman of the Judiciary Committee that approved the two articles of impeachment against the president that the House passed last month, is also widely expected to be a leader of the group. But for now, final decisions on the rest of the team remain unresolved.