It's the go-to network for outraged conservatives – but now Fox News has benched two high-profile pundits, and shown signs of retreat. Is the US's biggest cable news network going moderate?

For America's liberals, it is the tantalising cherry on top of the Obama election victory cake. The decision by Fox News to cut back the use of high-profile rightwing political pundits Karl Rove and Dick Morris raises a prospect few ever thought possible: that the hugely successful conservative cable news channel is in retreat.

In the wake of President Barack Obama's election win last month – which flew dramatically in the face of Rove and Morris's confident on-air predictions – the News Corp-owned station is being forced to adjust to a new reality.

Its broadcasting landscape is now one in which four more years of Obama's presidency stretch out in front of it. That second term was also won in an election many saw as a rejection of a Tea Party-infused Republicanism that saw extreme figures like pizza magnate Herman Cain, social conservatives Rick Santorum and Michele Bachmann and even business mogul Donald Trump briefly leading the Republican field.

As a result, some experts see Fox News as having emerged from the defeat of eventual candidate Mitt Romney in the same shape as the Republican party itself – with a somewhat tarnished image. "It was a damaging election for Fox, not so much down to the result, but in the way that it was handled in the weeks leading up to it and in Rove's famous on-air meltdown," said professor Jack Lule, a media expert at Lehigh University.

The incident Lule is referring to happened on election night itself when Fox regular Rove questioned the channel's own polling unit in deciding to call the crucial state of Ohio for Obama. In a remarkable piece of live television – ordered by Fox News' co-founder Roger Ailes himself – anchor Megyn Kelly and a camera crew then took Rove's opinion to the Fox decision desk who stood by their call and debunked Rove's doubts.

For some, including many critics of the channel, the incident became the key moment when Fox News' often barely-disguised championing of the conservative cause ran into the simple reality of the facts on the ground. It also went viral. "My sister called me up to say: 'Turn to Fox News. It's crazy'," said Webster University broadcast journalism expert Professor Eileen Solomon.

Since then – as the Republican party itself divides between senior voices calling for more inclusive policies and a still outraged conservative base – Fox News has shown several other signs of moderating its stance. Not only has it "benched" Rove and Morris – with senior management permission needed if any producer wants to put them on air – but some of its top personalities are shifting policies.

Just two days after the election, which Obama won with a huge majority among Hispanic voters, Fox host Sean Hannity told listeners to his radio show that his views on illegal immigrants had "evolved" and he now supported a path to citizenship. Regular Fox News pundit Ann Coulter has also changed gear. Just this week she revealed on Fox that she now supported tax rises on the wealthy as a political tactic.

The shifts might reflect Fox News' and Ailes' establishment position within the broader Republican party, where both are hugely influential. Indeed, a plethora of Republican bigwigs – from Mike Huckabee to Sarah Palin to Newt Gingrich – have been paid Fox pundits.

Fox's unease thus reflects a wider Republican nervousness among top donors and the party elite about demographic growth among minorities that could play into the hands of Democrats for many election cycles to come.

Even before the election Fox had ended the show of notorious host Glenn Beck, who had become known for postulating rightwing conspiracy theories and made several racial gaffes. Beck, too, had begun to fall out of favour with Republican leaders. "Roger Ailes is part and parcel of the GOP establishment. He has a guiding role. Fox is a part of the GOP machine as much as it is a media enterprise," said Tim Dickinson, a national affairs correspondent for Rolling Stone, who has written a lengthy profile of Ailes for his magazine.

But some warn that any liberal celebration over the idea of Fox moderating is more than premature. For example, Fox has enthusiastically pursued Susan Rice, Obama's preferred nominee to be the next secretary of state, for comments she made in the wake of a terrorist attack in Benghazi that killed the ambassador to Libya.

Many of its hosts and broadcasting is still resolutely critical of Obama, and offers a regular diet of red meat to its conservative audience. Indeed, some people expect Rove himself to eventually return to the channel on a regular basis. "With Rove, I think it is kind of like a "head fake" in basketball. They are not really under great pressure to fundamentally change," said Rick Edmonds, a media business analyst for the Poynter Institute.

That goes to the heart of what makes Fox tick, says Edmonds. Since being founded in 1996, Fox News has emerged to become the dominant force in cable news, and its political influence stretches far beyond its several million cable viewers. It is also highly profitable for its parent company. "If we do see any moderation it will be superficial. There will not be a sea change, because I don't think their advertisers or their viewers will demand that. Millions of conservatives like to watch and you can sell a lot of ads on the back of them," said Edmonds.

Fox News actually lost the battle for viewers on election night last month – the single most important event for the channel since the previous election – as CNN netted 8.8 million viewers to Fox's 8.7 million. But the fundamentals of the market have not changed. In November overall the most recent viewership figures show Fox easily dominated its rivals with a nightly average of 2.6 million during primetime. That means Fox News has occupied the number one spot for a remarkable 131 straight months.

At heart Fox News remains a business where the bottom line is just as important, if not more so, than the political line. And in a second Obama term, there is still a rich vein of conservative anger to be mined among core viewers. "If you are Fox you still need to feed the hardcore beast. It is possible that Ailes will guide viewers to a more moderate place, but it is not likely," said Dickinson.

Not that anyone at Fox sees it like that. The channel always insists it covers the news by its famed slogan "fair and balanced", and Ailes recently outlined his editorial philosophy in terms that would seem to dismiss any notion of problems in the wake of Romney's defeat. "I know no-one believes it, we have no agenda," Ailes said in a recent rare interview with the TVNewser blog. "I don't mind praising the guy (Obama) and I don't mind questioning the guy. It's day to day."