In Robert Schenkkan’s “The Great Society,” Lyndon B. Johnson wins the 1964 election but loses his soul and goes to hell. American cities burn, and Vietnam drags him under by the lapels of his rumpled gray suit; in Kyle Donnelly’s enveloping production at Arena Stage, the flames actually lick at LBJ from below.

“The Great Society” is Schenkkan’s sequel to “All the Way,” the Tony-winning drama that showed Johnson in full wheeler-dealer mode as he steered the Civil Rights Act to passage. Schenkkan is certainly interested in the legislative process, and the audience watched LBJ’s hardball negotiations with a double consciousness during Thursday night’s opening as the 2018 federal government shut down yet again.

But Schenkkan is primarily smitten with Johnson’s big ideas and blunt tactics, and the show is driven by Jack Willis’s performance — a growling, full-throttle turn with the energy of a Mack truck roaring downhill. Willis has inhabited this role since “All the Way” premiered at the Oregon Shakespeare Festival in 2012, and he’s a solid fit. His bluster has power, the profane wit is tart, and the conscience that plagues LBJ rings absolutely true.

Equally persuasive is the vindictiveness that finds Johnson turning increasingly to J. Edgar Hoover (a splendidly cast Richmond Hoxie, looking like a sour bloodhound). Schenkkan’s LBJ doesn’t really have partners: Everyone’s a chess piece, and scenes are engineered to show Johnson persuading or shoving them into place. A handshake is almost certainly a strong-arm in disguise.

“The Great Society” is a starry parade of 1960s figures zipping through the Oval Office at an almost zany pace — Robert McNamara with updates from Vietnam, Martin Luther King Jr. talking strategy about Selma, George Wallace holding his ground as the recalcitrant Alabama governor, Robert F. Kennedy and Johnson rubbing each other the wrong way. That’s a partial list, and Donnelly’s bewigged, drab-suited cast (costumed by Nan Cibula-Jenkins) does a credible job looking and sounding the parts.

A lot of the time, these figures simply deliver bulk information as Schenkkan keeps his narrative hustling through the entirety of Johnson’s term. But whenever the actors have time and space to make an impression, they take full advantage. JaBen Early delivers Stokely Carmichael’s “black power” argument vividly, Cameron Folmar is a distastefully smug Wallace, and John Scherer is a patrician-sounding RFK who plainly looks down on this president.

The show gains epic scale via the presidential seal on the floor of Kate Edmunds’s set, through lights by Nancy Schertler that sometimes shoot up through the floor and most notably from Aaron Rhyne’s projections on the outer walls of the in-the-round Fichandler space. (The bulk of the cast and design team is back from Donnelly’s 2016 “All the Way.”) Tallies of the body count in Vietnam, protest footage and Walter Cronkite’s game-changing “stalemate” verdict on the war are among the images bringing history to life.

Schenkkan’s script can make you shift and squirm when it resorts to shorthand — the too-comic manhandling of the American Medical Association, for instance, and trotting out Richard M. Nixon to kick around at the end. Like Margaret Thatcher in Moira Buffini’s dashing “Handbagged,” currently at Round House Theatre, Nixon declares his aim to make his country great again. It’s worth noting that audiences are now wearily groaning at these lines.

The fascinating thing is that Schenkkan’s portrait of an LBJ who increasingly compromised and lied evokes not only the Washington of the Pentagon Papers, but also Watergate, a thought that flickers even before Nixon shows up. It’s in Willis’s performance: He is magnificent with this character’s high and low style. He spins down-home anecdotes about snakes and bulls just right, and there’s a steely edge and assured cadence to Willis’s voice that makes the stage all his. It’s a performance with flash, but also the weight of tragedy.

You may not always believe in the satellite characters Schenkkan writes, but you buy this LBJ as he tries mightily to lift the country up exactly as he drags it into one of its blackest depths.

The Great Society, by Robert Schenkkan. Directed by Kyle Donnelly. Original music and sound design, David Van Tieghem. With Stephen F. Schmidt, Lawrence Redmond, Deonna Bouye, Elliott Bales, Craig Wallace, Megan Graves, Tom Wiggin, Desmond Bing, Bowman Wright, Gary-Kayi Fletcher, Andrew Weems, Susan Rome, Brook Berry, Eli El, Clayton Pelham Jr., Ben Ribler, Reginald Richard and Alana D. Sharp. About two and a half hours. Through March 11 at Arena Stage, 1101 Sixth St. SW. Tickets: $40-$110, subject to change. Call 202-488-3300, or visit