But as Shapiro and the play’s commercial producers mulled New York, many of the bankable male actors they considered didn’t “necessarily understand the joys of ensemble theater,” Letts said, noting that Superba shares the stage with an assortment of council members, adorned with similarly Dickensian names like Oldfield, Assalone, and Carp. (He says he stole the Superba name from a refrigerator.)

“You go through a few of those people and then you go, the hell with it, I’ll do it,” Letts said.

So it is that Letts — who won a Tony Award in 2013 for his take as George in “Who’s Afraid of Virginia Woolf?” — has been stumbling his way through rehearsals as an actor and then stumbling home to do rewrites as a playwright, trying to tweak the script while also cursing the writer.

“If I’d known that I was going to wind up doing it I wouldn’t have given him so many goddamn lines,” Letts said of Superba.

Letts’s fatigue, of course, has more to do than with just his performance: his son, Haskell, will turn 2 just days before Letts opens on Broadway, and just as his wife and Haskell’s mother, the actress Carrie Coon, finishes a revival of “Bug,” his 1996 creepy-crawly conspiracy comedy, at Steppenwolf.

The opening of “The Minutes” and the closing of “Bug” are scheduled for the same day, and Letts, a first-time father at 52, describes his family’s current chaos — toddler, rehearsal, performance, repeat — like “planning the battle of Midway everyday.”

Indeed, Coon, who fell in love with Letts as she played Honey in “Virginia Woolf,” says the current grind is so intense that Letts is threatening to retire, something she teases him about.