Rotund, bald and ferocious, the Fox television boss Roger Ailes is said to have two speeds – attack and destroy. Every night under his watch, millions of Americans are enthused, engrossed or appalled by a lively diet of angry rightwing rhetoric served up on Fox's rolling news channel. But the heady mix of hectoring, finger-pointing and liberal-bashing may be proving too spicy even for the strong stomachs of his employers, the Murdoch clan.

Matthew Freud

Rupert Murdoch's family, a close-knit, powerful and discreet dynasty scattered across three continents, prefer to air their dirty washing in private. Rumoured squabbles over inheritance, succession and over Murdoch's choice of wife have generally played out behind closed doors.

But a gaping crack appeared in the edifice of unity this week as Murdoch's son-in-law, Matthew Freud, delivered an astonishingly public broadside against Fox News. Freud, a media-savvy London public relations supremo married to Murdoch's daughter, Elisabeth, told the New York Times that members of the Murdoch family had become embarrassed by Fox's output: "I am by no means alone within the family or the company in being ashamed and sickened by Roger Ailes's horrendous and sustained disregard of the journalistic standards that News Corp, its founder and every other global media business aspires to."

Freud is said to be adamant that he was speaking on his own behalf, but he is also unrepentant. His words were calibrated to exert maximum damage and are a stunning blow to one of Murdoch's longest serving and most successful lieutenants. Their impact was all the more powerful because such moments of indiscretion are anathema to Murdoch, as one high-ranking former employee recalls. "When you are in the inner circle, you are expected to keep your mouth shut. The mafia call it omerta – the code of silence."

On the face of it, Freud's remark indicates a rift within the family. But some Murdoch-watchers believe it may be a more subtle signal. When Freud spoke, it was not his voice but Murdoch's that many media observers in the US and Britain heard. The author Michael Wolff, who recently penned a biography of Murdoch, believes Freud's outburst may be part of an orchestrated attempt to undermine a lieutenant who is getting a little too powerful. He points out that none-too-discreet "whispering campaigns" pre-empted the departure of other top executives.

"In many instances, it takes about a year to fire someone at a high level within News Corp. They kind of marginalise you, stop speaking to you and eventually you get the message that it's over."

A former political strategist who worked on the successful campaigns of three Republican presidents, Ailes was hired by Murdoch in 1996 to launch Fox News, in a widely scorned effort to challenge the broadcast establishment.

Some 14 years later, Fox is by far America's favourite specialist news channel, pulling in 2.1 million prime-time viewers every evening – more than its two main rivals, CNN and MSNBC, combined. In business terms, it is a jewel in the crown of Murdoch's global media empire, tipped to make $700m (£430m) in operating profit in a difficult year for News Corp. Hit by asset writedowns, the parent company made a loss of $3.3bn last year.

"Fox is a star performer, without a doubt," says Edward Atorino, a media analyst at Wall Street stockbroking firm Benchmark, and Ailes is a key piece in the News Corp jigsaw. "There aren't too many Roger Aileses around … If he were to leave, it would leave a huge hole."

With a pay package of $23m in 2009, Ailes made more money than Murdoch himself. Unusually, he has revealed that he personally lobbied Murdoch after hearing that his US papers might endorse Barack Obama. That irritated younger members of the Murdoch dynasty, while Fox's coverage of Obama since has left some of them horrified. Andrew Neil, who edited Murdoch's Sunday Times for over a decade and is also a former News Corp executive, says James Murdoch and Freud's wife Elisabeth both supported Obama, while Elisabeth raised funds for the Democrats. Neither are liberal, he concedes: "They just happen to be marginally more liberal than Rupert. It's a difference of tone."

Neil doesn't buy the theory that Freud was acting with Murdoch's consent, but agrees that "he is reflecting the views of the younger Murdochs". "What better way to let their liberal friends know they are upset about the way Fox News is behaving than on the front page of the New York Times, the liberal journal of record?"

Although promoted under the slogan "fair and balanced", Fox News horrifies political moderates with the hectoring rhetoric of its prime-time evening anchors. One man in particular, Glenn Beck, raises liberal hackles with his furious diatribes against Obama. Advertisers including Procter & Gamble and the insurer Geico withdrew commercials from Beck's nightly show in August when the anchorman accused Obama of being "racist" towards white people. Just this week, Beck used a blackboard and chalk to illustrate the supposed similarities of Obama's policies to those of the Venezuelan president, Hugo Chávez.

Beck is by no means unique. Conservative commentator Bill O'Reilly has used his primetime Fox show to label Mexicans immigrant "wetbacks". A passionate opponent of abortion, he was criticised last year after a Kansas abortion doctor, George Tiller, was murdered. Repeatedly dubbing him "Tiller the baby killer", O'Reilly had eviscerated him for operating a "death mill" and "executing babies" for profit.

Fox's weekend line-up also includes a chatshow hosted by the former Republican presidential candidate Mike Huckabee, while Sarah Palin was signed up this week as a political commentator.

Fox's style was inspired by America's legion of rightwing radio "shock jocks", according to Kerwin Swint, author of Dark Genius, a biography of Ailes. "It's very anti-government, very anti-establishment," he says. "Part of Ailes's philosophy for television is that it should be confrontational. That draws viewers, it's exciting for people and it's always been a staple of talk radio."

Irritated by Fox's partisan coverage, the White House has upped the ante. Obama has described the Fox network as "entirely devoted to attacking my administration" and has repeatedly snubbed its shows. The White House has been accused of failing to call on Fox journalists at press conferences and freezing the channel's reporters out on overseas trips. Obama's officials are unapologetic – Anita Dunn, former White House communications director, described Fox as "the communications arm of the Republican party".

Fox argues that during daylight hours its coverage is objective, drawing a distinction between daytime reporting and opinion-driven evening shows in the same way that newspapers distinguish between news pages and editorials. And Fox has a track record of breaking major stories – including news damaging to Republicans. But clashing with the White House may not help Murdoch's other business interests, and he has faced pressure to tone Fox down.

"He has members of his family riding him hard about this all the time," says Wolff, adding that Murdoch has become increasingly embroiled with the liberal "chattering classes" of Manhattan and Hollywood under the influence of his wife, Wendi Deng. "He spends a lot of time socialising with people who tell him rather constantly that Fox News is contemptible."

News Corporation was quick to dismiss the row this week, portraying Freud as an outsider. A spokeswoman said: "Matthew Freud's opinions are his own and in no way reflect the views of Rupert Murdoch, who is proud of Roger Ailes and Fox News."

Ailes himself sought to defuse any notion of a rift, telling the Los Angeles Times that "the entire Murdoch family" had always been supportive of him: "There is nothing to the idea that I have any problem with the children."

Jack Shafer of the website Slate suspects Ailes is getting too uppity for his boss's liking: "There's only one star in the News Corporation firmament and it's Rupert Murdoch. You succeed there by keeping your head down and working hard. Murdoch despises glory-grabbers." Neil, who was sacked by Murdoch, concurs. "He hates it when the hired hands get above themselves, so Ailes's days are numbered."

Murdoch will be flying to the Swiss ski resort of Davos in two weeks to rub shoulders with the world's business and political elite. Unusually, Freud won't be attending. Murdoch watchers may seize on that as evidence that Freud has been frozen out by Murdoch, at least for now. Ultimately, however, it may be the rumbustious Ailes who is left out in the cold.