“Isn’t that the best thing that ever happened?” asked Wilson, adding that her organization has spent years pleading with Hollywood honchos to write shows about a female president, only to be turned down. Then the one year the group did not lobby Hollywood, “The Contender” writer and director Rod Lurie created “Commander in Chief.” Tinseltown’s contribution is so vital, Wilson argued, “because we know that you can’t be what you can’t see.”

Before the screening began, there was a taped message from Davis herself, wishing the White House Project well and making a lame gag about how she’d love to be at the party in person, but that “being leader of the free world is a tough gig.” Ba-dum-bum. “We Americans love to think of ourselves at the top of any list,” Davis continued, “but we are 61st in the world in female representation in government, behind Rwanda and India and Slovakia. We can do better.”

By the time the hourlong show started, the crowd was pumped to respond to the story of Davis’ Mackenzie “Mac” Allen, an Independent (read: Democratic) veep to Republican prez Teddy Roosevelt Bridges, who suffers a brain aneurism and tells her — in a helpfully lucid moment just before he kicks it — that he wants her to step aside as president because “we just see a different America.” This is the kind of fundamental difference that really should have been considered when Teddy picked Mac to run with him. Instead we’re shown a flashback of that moment, and we learn that Mac spent four years in Congress before becoming chancellor of a major university. “How many Nobel Prizes have you won?” Teddy asks Mac over their get-to-know-your-running-mate lunch, before assuring her that her “expertise in Middle Eastern politics is impeccable.”

The Amazonian Davis is herself impeccable — just awesome, even in the cheeseball moments. And the show is not nearly as bad as it could have been. In the premiere, at least, there were none of the most dreaded scenarios: no instance, for example, in which President Mac has to decide between a Cabinet meeting and little Billy’s school play. (Though her youngest daughter does spill juice on her mother’s blouse just before Mac is supposed to address Congress. Why doesn’t that ever happen to daddy presidents?)

We see Mac capably putting the military on high alert, calling a Joint Chiefs of Staff meeting, firing her husband as chief of staff, and calling her Cabinet out about whether any of them have plans to resign.

The crowd in Caroline’s was wild for the stuff.

When Mac dresses down her predecessor’s chief of staff, telling him, “You’re not in a position to tell me how I take my coffee,” the audience let loose with a big old “Whoo-hoo!”

The evil conservative Speaker of the House Nathan Templeton — the man who would be president if only the tall chick would stand down — is played with unctuous perfection by Donald Sutherland. When he appeared on-screen, the crowd hissed — yes, hissed — their disapproval. Mac mocks Templeton’s arguments about why she should resign by saying, “We have that whole once-a-month will-she-or-won’t-she push the button” problem. Templeton responds, “Well, in a few years you won’t have to worry about that anymore.”

“Hissss.”

He then whales on her first act as president — the freeing of a Nigerian adultress about to be stoned to death — referring to the Nigerian prisoner as a “lady who couldn’t keep her legs together.”

“Hissssssssssss.”

Seriously, Donald Sutherland should get a bodyguard. This audience hated him with the passion of a thousand burning suns.

But it was Davis’ big moment. Templeton’s retro-malevolence is too much for her. She crumples her resignation and announces, “I am going to go out and protect the Oval Office.”

“Yes!” shouted the crowd. They also loved all the dithering about Mac’s husband’s role as First Lady. When the emasculated dude (played by Kyle Secor) is shown around his pink office and asked how big his staff will be, his chipper, nose-wrinkling secretary tips him off that “Mrs. Clinton had more than 20. That didn’t go over very well.” In the White House kitchens, he’s asked to confer on daily menus. “Of course, Mrs. Clinton shunned that,” says the secretary, adding unnecessarily: “That didn’t go over very well.”

The most crowd-pleasing moment came when the just-widowed former First Lady spouts one of those aphorisms often found in forwarded e-mails, telling Mac, “If Moses had been a woman leading the Jews in the desert, she’d have stopped and asked for directions. They’d have been in Israel in a week.” Har!

But just when it felt as if there would be no gender cliché unturned, the show hit a nerve. Mac enters the Capitol rotunda to address the nation; there are the familiar words: “Mr. Speaker, the president of the United States”; and then Thelma Dickerson walks through the door. The moment sent chills. The audience was sniffling. Some of them perhaps hadn’t been sure they’d live long enough to see this. Even on television.

As the show ended, Wilson took the stage, wiping a tear from her eye. “I must have seen this eight times,” she said, “and I keep trying to watch it without crying.”

She introduced the perennially black-clad Steinem. “One of the advantages of being an old person,” said Steinem, who is 71, “is that you see how far we’ve come.” She congratulated Marie Wilson for “going to Hollywood on her knees.” After a rumble of surprised laughter, Steinem — who’d clearly not meant that phrase to come out that way — looked as if she were considering an off-color joke but thought better of it. It probably wasn’t the right crowd. So she plowed on, asserting that she knew “in her heart of hearts” that a female president is on the horizon.

“We are so ready,” she said. “It’s only those guys, like that speaker of the house, who are not. So I say, ‘Fuck ‘em.’”

Preliminary ratings showed that the “Commander in Chief” premiere was a surprise hit, the top-rated show of the night.