Jack Willis, seated, as President Lyndon B. Johnson, surrounded by the ensemble of “All the Way.” (Stan Barouh)

“All the Way,” Robert Schenkkan’s Tony-winning drama about President Lyndon B. Johnson and the passing of the landmark Civil Rights Act of 1964, is a valentine to that sexiest of wonky Washington buzzwords: process. A civics lesson enlivened by LBJ’s rude tongue and Martin Luther King’s more eloquent one, the play explores at lavish length the glad-handing, bullying, bargaining and begging it took to get the historic legislation passed and set the nation on a more just and civilized path.

You’ll be grateful for Johnson’s salty way of putting things, because it’s the force of the 36th president’s personality that keeps this vehicle at Arena Stage from toppling. For this dramatic excursion, it seems, the playwright has overpacked, filling this quintessential D.C. story with a fatiguing amount of exposition. The tale of the bill’s passage, in fact, sees us over only half the ground the play covers; Act 2 chronicles the 1964 campaign for the presidency that followed Johnson’s ascension to the job a year earlier, after the assassination of John F. Kennedy.

Schenkkan seems to have been overly protective of the mountain of information he amassed, a result being that “All the Way” — like a term paper weighed down by footnotes — is almost too much.

Fortunately, the play’s vast hull has been built chiefly to contain the character of the wily Johnson himself, and he’s just entertaining enough to make “All the Way” worthwhile. On Broadway, the role was filled by Bryan Cranston, whose uncanny physical embodiment and comedic virtuosity proved irresistible. On Arena’s Fichandler Stage, the president is played by Jack Willis, recently the soothsaying bartender in the company’s production of Lynn Nottage’s “Sweat,” and who originated the role of LBJ when “All the Way” had its world premiere at the Oregon Shakespeare Festival in 2012.

Willis’s conception is of a more cantankerous, impatient Johnson, who snaps waspishly at wife Lady Bird (“Fix your lipstick!”) and coldly belittles his future vice presidential running mate, Hubert Humphrey (Richard Clodfelter). If Cranston’s LBJ was a stealthy tiger — whom you can see next month when HBO unveils its movie version of the play — Willis’s is a growling bear. Cranston may have been more fun to watch, and more effective at the voice and physical resemblance, but Willis’s portrayal works on its own terms, too, because the extraordinary tenacity tinged with insecurity that drove Johnson is as vital a component of Willis’s performance as it was of Cranston’s.

(L to R) Jack Willis as President Lyndon Baines Johnson and Bowman Wright as Martin Luther King, Jr. (Stan Barouh)

That it took a Southern politician to bring the South’s historically discriminatory laws to heel is one of the more remarkable thematic linchpins of the play. Johnson grew up dirt poor in the Hill Country of Texas, Schenkkan has LBJ tell us, and it was his knowledge of privation that seems to have endowed the president with a compassion for the struggles of African Americans that many of his colleagues lacked. Lovers of U.S. political history will enjoy the academic streak running through the play, because it is in part an illuminating account of the birth of the Republican Party’s “Southern strategy”: Alienated by Johnson’s determination to move the nation forward on civil rights, traditionally Democratic Southern voters and officeholders began a migration to Republicanism that continues to have an impact on national politics to this day.

With its panoply of famous names from the Johnson era, and an attendant assortment of story lines, “All the Way” potentially could feel like a newsmakers’ pageant. Such varied people out of the headlines of the ’60s as J. Edgar Hoover (Richmond Hoxie), George Wallace (Cameron Folmar), Stokely Carmichael (Jaben Early), Robert McNamara (David Bishins) and Ralph Abernathy (Craig Wallace) waltz prominently through “All the Way.” Staging the production in the round at Arena, director Kyle Donnelly comes up with a far more fluid game plan for the narrative than director Bill Rauch achieved in the Broadway version, where actors sat at desks, as if they were all part of a deliberative body.

Here, on set designer Kate Edmunds’s turntable platform, emblazoned with the presidential seal, the long parade of scenes flows more muscularly, with actors and a few spare set pieces smoothly establishing each of the public and private moments. The costumes by Nan Cibula-Jenkins vividly evoke the period, even if the production places an emphasis on men in boxy suits, and David van Tieghem’s crisp sound design is a special blessing.

Among the most memorable of the supporting performances are Hoxie, as a constipated Hoover; Lawrence Redmond, as a dignified Richard Russell, the Georgia senator who was Johnson’s friend and adversary; and Bowman Wright, whose Martin Luther King must contend within his movement with the same kind of battling factions Johnson faces in the White House. Female characters are fewer and farther between in this tale, although Susan Rome makes the most of her scenes as Lady Bird and Shannon Dorsey does well as Mississippi civil rights activist Fannie Lou Hamer.

The most powerful take-away, though, from the nearly three hours of “All the Way” is the success of Johnson’s command of the process. You might even say that the real star of the show is the art of compromise itself. To fully communicate this, the play does sacrifice some emotional texture. But like the president at its center, “All the Way” ultimately does get the job done.

All the Way by Robert Schenkkan. Directed by Kyle Donnelly. Set, Kate Edmunds; costumes, Nan Cibula-Jenkins; lighting, Nancy Schertler; original music and sound, David van Tieghem; projections, Gregory W. Towle; wigs, Anne Nesmith; dialects, Mary Coy. With John Scherer, Adrienne Nelson, Tom Wiggin, Stephen F. Schmidt, David Emerson Toney. About 2 hours and 50 minutes. Tickets: $40 to $90 (subject to change based on availability). Through May 8 at Arena Stage, 1101 Sixth St. SW. Visit arenastage.org or call 202-488-3300.