Michael Murphy’s paralyzingly dull “The Conscientious Objector” achieves the impossible — it makes a preacher, Martin Luther King Jr., and a president, Lyndon Baines Johnson, sound nearly indistinguishable.

The play delves into the last years of King’s life, after his most famous speeches were behind him and the hard job of implementation had begun. The iron was hot, but an enormous amount still needed to be hammered out, including registration protection and open housing. But King (D.B. Woodside) heard another call. Appalled by the casualties in Vietnam, he used his bully pulpit to rage against the war. The hero of Birmingham became a pariah: The rest of the civil rights movement drew away in horror, and his relationship with LBJ (John Cullum) turned sour. King, forged in a black-and-white struggle against patent injustice, now tested his mettle against an ugly public backlash and the gray realities of foreign involvement.

Mr. Murphy finds the silver lining in the widespread clandestine wiretapping of the time by borrowing liberally from the transcripts of taped phone calls and the CIA’s covertly placed bugs. (This may be the first time a playwright owes thanks to J. Edgar Hoover.) The play therefore consists of bullpen sessions among King’s team (including Bryan Hicks as Ralph Abernathy and Steve Routman as Stanley Levison), strategy sessions between Hoover and LBJ, and various selections from op-eds, television interviews, and public speeches. No doubt Mr. Murphy has done his homework, but he cannot effect the basic artistic alchemy of making it not sound like homework.

How does it go wrong? We see men in the grip of incredible forces — LBJ weeps over the casualty reports he reads every morning, and MLK staggers like Atlas under his astonishing burdens. We should be witnessing the Olympians of the modern age. Practically, though, Mr. Murphy spends his 2 1/2 hours in haphazard biography rather than in any kind of dramatic movement. Arguments never develop; positions never change. When King does change his mind about something, it happens arbitrarily, as we never penetrate his thoughts. We wind up understanding him about as well as the eavesdropping Hoover.

Rescue might have arrived had the actors developed a winning, familial sense among themselves, but they never did. In fact, desperate for footing, each relies on his backup style. For the more experienced actors, this results in tiny successes: In a variety of small, sleazy, white-guy roles, Jonathan Hogan underplays slyly, and, should he pick up speed, Mr. Cullum may yet borrow some of Johnson’s hearty charm. But, left unprepared by his TV acting gigs, Mr. Woodside offers us a performance as emotive as a brick fireplace — with none of the heat. Rachel Leslie’s Coretta stares vacantly at him, and Mr. Hicks pouts unstintingly, but Mr. Woodside out-stonewalls them all.

The play’s pedantry is, unfortunately, complemented perfectly by the production.

Beowulf Boritt’s chalky, cheap-looking black-and-white set consists of an enlarged American flag that covers the back wall and floor and a few shiny aluminum chairs. Theresa Squire does an equally dogged job with the costumes — identical rows of black suits and ugly ties. But ultimate blame must rest with the director, Carl Forsman, who lets the pace go from leaden to tar-pit.

Throw Mr. Forsman at a mid-century American classic (his Keen Company’s specialty) and his straightforward touch results in refreshingly unpretentious work. But here the complexity of the directorial task overwhelms him. The unwieldy text needed a braver hand, and the relationships needed a lighter one. Instead, Mr. Forsman and Mr. Murphy throttle out our history with clenched, suffocating earnestness. The show needs energy, air, rhythm, and life. It’s a pity that King would have been the first to tell them that an open palm always works better than a closed fist.