With a single word, Megyn Kelly managed to turn a cringe-inducing election night moment on Fox News into an entertaining one.

“AWK-ward,” she said.

Kelly was coanchoring the coverage, and Fox analyst Karl Rove had just challenged his own network’s projection that President Obama would win Ohio, and with it the presidency. Kelly added a note of humor as things were turning uncomfortable, then walked down a long hall to chat with Fox executives on why they made what turned out to be the right projection.

Kelly has emerged as a breakout star at Fox after a campaign in which she helped moderate a number of high-profile presidential debates. And that has created a bit of a dilemma for the network, as her contract is up next summer.

She is clearly too big a talent to remain marooned at 1 p.m. and would like a more prominent time slot. But with Fox having stuck for years with a winning prime-time lineup of Bill O’Reilly, Sean Hannity, and Greta Van Susteren, it is not clear where Kelly would land.

Kelly, who began her career as a lawyer, is far from a cookie-cutter anchor. The 41-year-old has two small children and was breastfeeding her baby during breaks in the prep sessions at a GOP debate in Florida last year. She went on Howard Stern’s radio show and calmly fielded a raunchy sex question. She did a sultry photo shoot for GQ in which she lowered the strap on a low-cut black dress, later telling friends there was nothing wrong with being a sexy mother.

Kelly, who was taking a break and could not be reached, once told me that “in the industry, women have a hard time because there’s an assumption that maybe you’ve moved up for reasons other than your mind.”

Michael Clemente, Fox’s executive vice president, likens Kelly to Katie Couric and Barbara Walters in terms of her ambition and tenacity. And he says her legal skills are a huge asset.

“She knows exactly how to find the heart of a story within moments, which is like finding the heart of a big case,” Clemente says. “She’s comfortable with herself on the air. She has a nice personality and she’s telegenic.”

Kelly is also a good match with her more serious election night partner, Bret Baier. “She sort of plays the goof a little bit and he plays off her,” says Clemente.

Bill Hemmer, who coanchored a morning show with Kelly, adds: “Megyn’s got it all. She’s supersmart.”

Kelly has been carefully groomed by Fox, which is keen to preserve her reputation as a fair and balanced anchor. Sometimes when she gets too opinionated during a segment, Roger Ailes, the network’s chairman, later suggests that she tone it down.

At the same time, there is no question that Kelly shares the Fox view of the mainstream media. She told me at the Republican convention that “there’s a little bias” in the mainstream media assessment “that [Mitt] Romney has difficulty coming off as a real person.” As for the coverage of Obama, Kelly said that “much of the press is still hoping that they were right the first time around. That’s the danger of planting an ideological flag as a reporter.”

She is not shy about pushing back. On election night, Kelly did more than make light of the contretemps with Rove, the former Bush White House aide who founded a super PAC that spent more than $100 million toward Romney’s election. As Rove insisted that Romney could still win Ohio, she asked: “Is this just math that you do as a Republican to make yourself feel better?”

Clemente was pleased when Kelly interviewed members of Fox’s decision desk, who insisted their Ohio projection was accurate. “I knew that Rove was on the phone with the Romney people,” Clemente says. “Megyn, when she’s going after information, she’s pretty pointed.”

At the same time, Clemente doesn’t fault Rove for arguing about Ohio. “The fact that it didn’t fit with the decision desk narrative, who cares? Open the door.”

The next day, on Kelly’s show, Rove charged without evidence that Obama had won reelection “by suppressing the vote.” Kelly wasn’t buying, reminding Rove that the president had won, period.

Earlier this year, Kelly got into a fierce argument with Fox contributor and Daily Beast columnist Kirsten Powers over Kelly’s intensive coverage of an investigation involving the New Black Panther Party. During the interview, Kelly kept raising her voice and interrupting Powers. “I was wrong to get angry and treat a guest so disrespectfully. I later apologized to Kirsten,” Kelly said afterward.

In a Newsweek interview, Kelly told me she was badly bullied by a group of girls in seventh grade and spent years overcompensating by trying to project an invulnerable exterior. “I slowly came to grips with the notion that my bravado was having the opposite effect than I intended,” she said.

Kelly, who grew up outside Albany, N.Y., got so bored being a corporate lawyer that she took some journalism classes, moved to Washington in 2003, and persuaded the local ABC affiliate to take her on as a part-time freelance reporter.

Within a year, she was being interviewed by Brit Hume, then Fox’s Washington managing editor, who hired her even though he didn’t have a job opening. Hume says she was “strikingly attractive,” had a “tremendous air presence,” and “came in believing there was a left bias in the news.” Kelly specialized in reporting on legal issues before being summoned to New York as an anchor.

In theory, Kelly could jump to another network next year. But she is grateful to Ailes for nurturing her career, so chances are Fox will figure out how to find her a bigger platform.