Once that complaint came out, alleging a scheme by the president to enlist Ukraine to help him in the 2020 election, Mr. Schiff led the investigation that resulted in the president’s impeachment for pressuring Ukraine to investigate his political rivals.

Strait-laced and slightly nerdy, Mr. Schiff tightly controlled the divisive process.

When Representative Matt Gaetz, Republican of Florida, muscled his way into a closed-door hearing without invitation, Mr. Schiff calmly told him to “absent yourself.” When two dozen Republicans stormed the secure hearing room, accusing Mr. Schiff of running a secret “Soviet-style process,” he suspended the session rather than create the spectacle of having his colleagues removed by Capitol Police.

“He’s a full package,” Ms. Pelosi said in an interview last fall, adding: “He knows his purpose. He knows his subject. He always thinks strategically, and he respectfully connects with people.”