With his rich baritone hinting of the American West and craggy handsome looks, Bryan Cranston seems custom built to play outsize heartland characters. Where was he, you wonder, when Sam Shepard was writing “Buried Child” and “True West”? Even at his most relaxed, when he leans in and taps your knee to drive home a point, you don’t want to be caught spacing out.

Mr. Cranston did star in Mr. Shepard’s “The God of Hell” in Los Angeles in 2006 — just before his career-defining transformation into Walter White, the chemistry teacher turned drug lord and high executioner he played for five seasons on the hit AMC series “Breaking Bad.” But apart from that, he’s done relatively little theater, and none at all in New York, which raises the stakes for his Broadway debut in “All The Way,” a three-hour production in which he’s onstage as Lyndon Baines Johnson almost every minute.

Filled with arcane talk about “discharge petitions” and “procedural votes,” “All the Way” is not standard Broadway fare. But beyond Mr. Cranston’s star power, the producers are also counting on timing: The story of a ruthless president who got things done — without blinking at the costs and compromises — reminds us that partisan gridlock doesn’t have to be a permanent condition.

“I think audiences are hungry for a play of this size and ambition,” said Robert Schenkkan, the playwright. “Everybody loves the four-character dining-room play about marriage. But there’s something about 20 bodies on the stage wrestling in this muscular visceral way with the political issues that still haunt us.”