What would he have to do to lose his viewers?

With repercussions from the sexual harassment allegations against Bill O’Reilly rippling through the country this week, Kimberly JaJack, a longtime Fox News enthusiast, descended into her basement on Wednesday, curled onto the sofa and clicked on the television.

Mr. O’Reilly, the star she calls her primary news source, beamed into the room, already barreling into the questions of the day on “The O’Reilly Factor,” the nation’s No. 1 cable news show. “Caution!” he said, like a sportscaster gearing up for a bout, as he offered up his signature opening, “you are about to enter the no spin zone!”

At a commercial, Ms. JaJack, 53, released the sigh of a conflicted woman. “Sexual harassment, that’s not something you turn a blind eye to,” she said, gripping the remote. “But what has happened? Is it going to be enough for me to say I’m not watching Bill O’Reilly anymore?”

Similar scenes played out across the nation this week, as fans of Mr. O’Reilly wrestled with the news, disclosed in a New York Times report last weekend, that he had reached settlements totaling about $13 million with five women who accused him of harassment.

Should they believe the women and drop Mr. O’Reilly from their TV news diet? Ignore the women and stay loyal? Or recognize that it could all be true and forgive him?

For Ms. JaJack, a black evangelical Christian who said she often feels alone in a family of Democrats, the allegations about Mr. O’Reilly posed a particular test. She did not love how the host had covered the Trayvon Martin case (“Slanted” in favor of the gunman, she said.) Or how he recently mocked the hair of Maxine Waters, a black congresswoman. (“Very inappropriate,” she said.) And she certainly does not condone sexual harassment.

She said she learned of The Times’s report through a news alert on her phone. “I don’t want to say it’s the norm,” she said of her reaction, “and I don’t believe in that. Because I don’t believe all of this is acceptable behavior. But it’s just like, it doesn’t surprise me.”

Mr. O’Reilly has been her beacon for current events, guiding her through turbulent and sometimes lonesome political waters since she became a Republican around the year 2000. “Some probably think he’s a little arrogant,” she said, sitting on a couch where she has watched him so many nights that the cushion bears a comfy indent. “But I find that he stays focused on the issue at hand.”

As an example, she noted how in an early segment Wednesday evening, Mr. O’Reilly had directed a guest away from discussion of a possible connection between Donald Trump’s presidential campaign and Russia, and toward his topic of choice: Whether the Obama adviser Susan Rice was, in the host’s words, “using her position with President Obama to surveil and hurt Mr. Trump.”

Ms. JaJack likes that Mr. O’Reilly has focused on the issues of illegal immigration and the attack on an American diplomatic outpost in Benghazi, topics she believes other news organizations overlooked. She supplements her media diet with Politico, The Washington Times and The Wall Street Journal.

“I’m not saying he’s pure,” Ms. JaJack said of Mr. O’Reilly, who has said the allegations against him have no merit. “Nobody is, including myself. But for the most part, I don’t hear him belittle people or talk down on people. He speaks from the left. He speaks from the right. And he’s giving you his experience, his knowledge.”

Mr. O’Reilly, now 67, joined Fox News in 1996, drawing both fans and critics with his pugnacious style and conservative bent. In 2015, the show brought about $178 million in advertising revenue to Fox News, according to Kantar Media.

About 80 percent of Mr. O’Reilly’s viewers are over the age of 55, according to data from Nielsen, a trend that has held steady for years. Men make up 54 percent of the audience, Nielsen said.

And Mr. O’Reilly’s audience is growing. So far this year, his total viewers are up 23 percent from last year’s average. His shows this week, since the Times’s article appeared, are drawing about 10 percent more viewers compared with a week ago, Nielsen said.

Ms. JaJack says she likes Mr. O’Reilly’s focus on the issue of immigration. Nick Cote for The New York Times
In interviews, other O’Reilly fans said the harassment claims would not sway them from Fox News or Mr. O’Reilly, whether or not the allegations are true.

In downtown Denver, a financial analyst named Shelli Barkley, 58, stood in the shade outside her office on a recent morning. She said she was “skeptical” of the veracity of the allegations against Mr. O’Reilly. She added that the host’s interactions with women might have been misunderstood. “We’ve all done things we regret. One person’s sexual harassment is another person’s flirting.”

Along with a friend, Sue Thielen, 52, Ms. Barkley said that she would continue to watch Mr. O’Reilly several times a week.

A few blocks away, Tom Miller, 67, sat at a picnic table with his wife, Sheryl, and their dog Magic. Fox News is a key information source for the couple.

“If that occurred, I don’t agree with it,” Mr. Miller said of the harassment claims, suggesting that an appropriate action would be a temporary suspension of Mr. O’Reilly.

But Mr. Miller said he had trouble believing the allegations. “The news is so skewed nowadays, it’s pathetic,” he said.

Ms. JaJack grew up here in the Denver suburb of Aurora, surrounded by Democrats. Around 1994, she became a born-again Christian, a transformation that eventually spurred her to join the Republican Party. She opposes abortion, she said, and that issue most informs her vote.

She lived in the Washington, D.C., area for many years, working contract jobs as a scheduler, administrator and management analyst in the federal government before returning to Colorado to help her mother. She served as an alternate delegate for Mr. Trump at the Republican National Convention, and then voted for him in the fall.

She said she that she had not paid much attention to the details about the sexual harassment allegations, and that she had no idea if they were true. Then a reporter told her about Wendy Walsh, a former regular guest on Mr. O’Reilly’s show, who said that the host invited her to his hotel room and then, when she declined his invitation, reneged on an offer to secure her a lucrative position with the network.

Ms. JaJack expressed sympathy for Ms. Walsh, but said that such behavior is part of the working world.

“I think that probably happens to many of us,” Ms. JaJack said.

Later in the conversation, though, she struck a more disapproving tone.

“If it’s happening,” she said, “they’re going to have to learn to either change their culture or change the men’s attitude.”

“It’s not right,” she continued. “No ma’am. I don’t care if it’s Fox, I don’t care if it’s CNN, I don’t care if it’s the White House and the president. It’s not right. Point blank.”

On television, Mr. O’Reilly was wrapping up his show with a pitch for a coming tour.

“Please remember, the spin stops here,” he said, pointing a pen at Ms. JaJack in the basement room. “We’re definitely looking out for you.”

Afterward, with her great-nephew bouncing on her hip, Ms. JaJack said she would not stop watching the show.

“Some people lose their way,” she said, speaking directly to Mr. O’Reilly. “I accept you because I believe in you. And believe in Fox News.”