NEW YORK — Before theater critics were invited to “Hillary and Clinton” on Broadway last month, the production made an unusual offer to the two people who above all others might have been expected to rake it over the coals.

“Bill and Hillary should have the chance to see it, but there’s no way they can sit in an audience in a Broadway house and watch this,” says actor John Lithgow, who plays the former president in Lucas Hnath’s new comedy-drama. “So we offered to perform it for them in an empty theater, just before we opened.”

Imagine it: The Clintons alone together — maybe holding their breath, or holding hands, or even holding their hands over their eyes — as Lithgow and Laurie Metcalf portrayed them and their eternally puzzled-over marriage. What would they make of a play so blatantly trying to define their relationship, a partnership that has unfolded over the decades as something closer to a rough crossing than a sun-dappled cruise?

We may never know. Though the Clintons were given an advance peek at the script, they declined the invitation to come, Lithgow says. Learning this, one’s curiosity about the life they have led together only intensifies.

“Look, I read the script and I wanted to be in it,” Lithgow adds, “but my immediate anxiety was, ‘What were these two people going to think?’ Because I admire them, I know them, I care about them.”

Peter Francis James plays Barack Obama and John Lithgow plays Bill Clinton in “Hillary and Clinton.” (Photo by Chris Sorensen)

Like the other actors in the 80-minute play — Metcalf, Zak Orth, portraying Hillary’s then-pollster, Mark Penn, and Peter Francis James, who makes a princely entrance late in the proceedings as Barack Obama — Lithgow decided that the opportunity was too intriguing to pass up, as long as it wasn’t an exercise in character assassination. This isn’t, after all, the first time a writer has portrayed the couple’s turbulent alliance. Joe Klein famously sought to reveal it in his roman-a-clef “Primary Colors.”

“We think, ‘Why are they together?’ And Lucas has the nerve to address it in the play,” Metcalf says. “We all just wanted to make sure that it wasn’t done with a wink, that it was respectfully portrayed, and with as much empathy as possible. Because we all feel that.”

The cast, which under Joe Mantello’s direction brings to life Lucas’ story – set immediately before and after the 2008 New Hampshire Democratic presidential primary — gathered recently in New York to talk about playing political figures whom an audience may feel they know well. From the discussion, one better understood the degree to which “Hillary and Clinton,” at the Golden Theatre, owes much to the power of Greek drama. It’s an account of two destinies, forever interlocked and yet forever in conflict.

“Laurie and I play these two characters who have two parallel, contradictory, cautionary tales in their lives,” Lithgow says. “Bill’s tale is: Careful what you wish for — you may get it. And hers is: Careful what you wish for — you may never get it.”

Metcalf has earned a Tony nomination for her portrayal of Hillary, who begins the play wistfully addressing the audience about the peculiar fate to which she has been relegated, never achieving what so many thought was in her grasp. Her brutally raw performance is tinged with gallows humor, melancholy and rage — attitudes and emotions to which Metcalf acknowledges she’s professionally drawn.

Laurie Metcalf, who plays Hillary Clinton, discusses the play with John Lithgow and other cast members in New York. (Photo by Chris Sorensen)

In 2017, she won a Tony as Nora in Hnath’s “A Doll’s House, Part Two,” who returns years later to the family she deserted in Henrik Ibsen’s 1879 proto-feminist masterpiece, “A Doll’s House.” A second Tony followed last year, for Metcalf’s turn as the middle-aged version of a dyspeptic dowager played by Glenda Jackson in a revival of Edward Albee’s “Three Tall Women.”

Like “A Doll’s House, Part Two,” “Hillary and Clinton” is a play about a strong woman contending with the emotional yoke of a controlling and, in Hillary’s case, unfaithful husband. But while Nora left, Hillary stayed, a difference that “Hillary and Clinton” chalks up in part to political pragmatism. Hillary is so hungry for an electoral win in New Hampshire – she’s already lost the 2008 Iowa caucuses to Obama — that over Penn’s vehement objections, she asks Bill to come to the state to help her.

“You have to root for those people where the odds are so stacked against them,” Metcalf says, referring to Nora and, especially, to Hillary. “I think for the audience also, it’s like, ‘How many things does she have to go through before something goes right?’ And yet she keeps coming back, and fighting and fighting. I like those characters – they’re so committed and passionate. To a fault, sometimes.”

It appears that in an early draft, the Mark Penn character was a particularly potent foil for Bill: “It’s a triangle,” Orth says. “I don’t want the husband there; he doesn’t want me there.” This carried a romantic dimension, one that is hard to visualize. “In one of the early versions — we never read it, it was gone by the time we came — Mark had kissed Hillary,” Metcalf says, laughing loudly.

“And Mark and Bill had a knockdown, drag-out physical fight,” Lithgow says. (It’s enough that what has remained in the play is a partially undressed Bill Clinton, emerging from the commode. “To see Bill walk out of the bathroom, you think, ‘Oh, my God, they go to the bathroom,’ ” Metcalf says.)

What also remains, though, is a truth apparent in every public relationship — that the private reality has depths that no one on the outside can fully grasp. James says that a cousin of his from Wisconsin, of a conservative political stripe, came to see the show. “I did not think it was possible to feel empathy for Hillary Clinton,” James reports him saying afterward. “I don’t sympathize with her. But I did empathize with her.”

Obama’s character has a different function in the play; he arrives in Hillary’s hotel room to disclose his pique at the tactics Bill has used to engineer Hillary’s surprise New Hampshire win. A messianic air is evident in James’s portrayal, as if he were a deity out of a medieval mystery play. To James, this Obama is a manifestation of what Hillary aspires to be: the Anointed One.

“I thought,” James says, “it was Lucas’ way of saying that maybe, there are universes in which Hillary loses, but there aren’t universes in which Obama loses.”

All through “Hillary and Clinton” are moments when the seemingly fundamental unfairness of the universe is clear: that there is a gap in fortune between Bill and Hillary that can never be bridged. The psychic pain resounds too loudly for her to bear hearing him.

“She has a hard time listening to what his take on how she should run her campaign should be,” Metcalf says. “Very hard time. I mean some of it’s at the meat of their marriage, too. He wants something from her that he has to dictate through the campaign.”

“My most piquant line is: ‘It’s never not emotional,’ ” Lithgow adds. “People don’t vote with their brains, even the people who think they do, don’t. It’s never not emotional.”

Metcalf replies: “One of the things we hit on with her is that it has to be about merit. It can’t be about anything else or it’s not fair.”

Talking about how Hillary navigated her political life reminds Lithgow of another sequence that was trimmed from the final version, in which Hillary asks Bill: “What if it had been different?”

“Switched around,” Metcalf elaborates. ” ‘What if instead of me supporting you, it had been you supporting me? All of those years. Did we ever consider that possibility?’ ”

Lithgow can’t recall how Hnath had Bill reply. Maybe that’s because the response would have been superfluous. We all assume we know the answer.