WASHINGTON — From Jimmy Stewart’s fictional all-night talkathon to real-life dramas over World War I and civil rights, the Senate’s filibuster has played a notable — sometimes reviled — role in the nation’s history. Now the slow-moving, famously deliberative chamber is on the verge of dialing it back — modestly.

Filibusters are procedural delays that outnumbered lawmakers use to try killing bills and nominations. But they seldom look like the speech delivered by the exhausted, devoted senator portrayed by Stewart in the film, “Mr. Smith Goes to Washington.”

In fact, the Senate has more filibusters than ever these days. But you’d hardly know it by watching the chamber on C-SPAN television....