The word “great” has many meanings, but, in History Theatre’s production of “The Great Society,” the main one is “enormous”: The three-hour-long play stretches over four years, with 17 actors playing more than three dozen people.

There’s some wobbly acting in the smaller parts, but the play, set during Lyndon Baines Johnson’s second term as president from 1965-69, is kept aloft by a fine trio of leads: Andrew Erskine Wheeler’s reluctantly conciliatory Vice President Hubert H. Humphrey, Shawn Hamilton’s dignified but passionate Rev. Martin Luther King Jr. and, especially, Pearce Bunting’s charismatic Johnson.

Bunting looks nothing like Johnson but, scrunching up his chin so his lower lip covers the upper, furrowing his brow, squinting his eyes, fiddling with LBJ’s signature glasses and spraying as much spit as invective, he convinces us he’s a dead ringer.

Robert Schenkkan’s play — a sequel to “All the Way,” which the theater performed last year — is a long day’s journey into night, hovering between reality and surreality. Although it takes place on an Oval Office set, that office stretches to become everything from Alabama to Los Angeles. People who would never have been to the Oval Office wander in and out, while huge placards on the back wall remind us — and LBJ — of mounting deaths in Vietnam. As if we’re the Ghost of Christmas Past and LBJ is Scrooge, we peer into his soul as he confronts the disastrous choices he has made. And Bunting responds with a magnetic performance that suggests LBJ was a vaudeville showman, a master manipulator and, ultimately, a failure.

There’s a tragic element to Johnson’s downfall, especially since, as he tells Lady Bird Johnson, “I did this.” But Schenkkan’s unwieldy play has trouble making the story dramatic. With a second act that is longer than its first and with Schenkkan unable to find an effective way to end either of them, this piece of docu-theater has an unfinished, misshapen quality. (The first act closes with the Watts Riots, which feels tangential to this story, and the play concludes with a dumb Nixon joke that cheapens the evening.)

Director Ron Peluso does what he can to shape the material, particularly in a suspenseful scene when LBJ’s advisers and friends gradually move closer and closer, creating a ring around him almost like the betrayers in “Julius Caesar.” And the play has many gorgeous individual moments. Darrick Mosley makes his occasional appearances count, whether it’s as fierce Stokely Carmichael or bewildered Jimmie Jackson, whose death helped inspire the Selma/Montgomery march. As Sally Childress, LBJ’s assistant, and Coretta Scott King, Jamila Anderson also contributes a powerful double whammy.

Women barely factor into the old boys’ club of LBJ, which is part of the point. Some of the things that challenged LBJ still dog us right now, including threats to black citizens’ right to vote, government that does not seem to represent many of its people and politicians who value party over morality. As if to make the connection between past and present, “The Great Society” opens with an image of LBJ at his desk, the stage surrounded by more than a dozen people: all of them men, most of them white and nearly all of them over 50. Whatever else Americans take away from current events, they’d have to agree that the makeup of power hasn’t changed much in 50 years.