Whoever wrote the political rulebook needs to start rewriting it. It used to be an iron maxim that voters' most vital organ was neither their head nor their heart, but their wallet. If they were suffering economically, they'd throw the incumbents out. Yet in Britain a coalition presiding over barely-there growth, rising unemployment and forecasts of gloom stretching to the horizon is holding steady in the opinion polls, while in the US Barack Obama is mired in horrible numbers – except for the ones showing him beating all-comers in the election now less than 11 months away. Even though the US economy is slumped in the doldrums, some of the country's shrewdest commentators make a serious case that Obama could be heading for a landslide victory in 2012.

How to explain such a turnaround? In the United States, at least, there is one compellingly simple, two-word answer: Fox News.

By any normal standards, Obama should be extremely vulnerable. Not only is the economy in bad shape, he has proved to be a much more hesitant, less commanding White House presence than his supporters longed for. And yet, most surveys put him comfortably ahead of his would-be rivals. That's not a positive judgment on the president – whose approval rating stands at a meagre 44% – but an indictment of the dire quality of a Republican field almost comically packed with the scandal-plagued, gaffe-prone and downright flaky. And the finger of blame for this state of affairs points squarely at the studios of Fox News.

It's not just usual-suspect lefties and professional Murdoch-haters who say it, mischievously exaggerating the cable TV network's influence. Dick Morris, veteran political operative and Fox regular, noted the phenomenon himself the other day while sitting on the Fox sofa. "This is a phenomenon of this year's election," he said. "You don't win Iowa in Iowa. You win it on this couch. You win it on Fox News." In other words, it is Fox – with the largest cable news audience, representing a huge chunk of the Republican base – that is, in effect, picking the party's nominee to face Obama next November.

This doesn't work crudely – not that crudely, anyway. Roger Ailes, the Fox boss, does not deliver a newspaper-style endorsement of a single, anointed candidate. Rather, some are put in the sunlight, and others left to moulder in the shade. The Media Matters organisation keeps tabs on what it calls the Fox Primary, measuring by the minute who gets the most airtime. It has charted a striking correlation, with an increase in a candidate's Fox appearances regularly followed by a surge in the opinion polls. Herman Cain and Rick Perry both benefited from that Fox effect, with Newt Gingrich, the former House Speaker, the latest: in the days before he broke from the pack, Gingrich topped the Fox airtime chart. Meanwhile, Mitt Romney cannot seem to break through a 20-to-25% ceiling in the polls – hardly surprising considering, as the league table shows, he has never been a Fox favourite.

But it works in a subtler way than the mere degree of exposure. Fox, serving up constant outrage and fury, favours bluster over policy coherence. Its ideal contributor is a motormouth not a wonk, someone who makes good TV rather than good policy. Little wonder it fell for Cain and is swooning now for Gingrich – one of whom has never held elected office while the other messed up when he did, but who can talk and talk – while it has little interest in Romney and even less in Jon Huntsman, even though both have impressive records as state governors. The self-described conservative journalist Andrew Sullivan says that the dominant public figures on the right are no longer serving politicians, but "provocative, polarising media stars" who serve up enough controversy and conflict to keep the ratings high. "In that atmosphere, you need talk-show hosts as president, not governors or legislators."

Fox News and what Sullivan calls the wider "Media Industrial Complex" have not only determined the style of the viable Republican presidential candidate, but the content too. If one is to flourish rather than wither in the Fox spotlight, there are several articles of faith to which one must subscribe – from refusing to believe in human-made climate change, and insisting that Christians are an embattled minority in the US, persecuted by a liberal, secular, bi-coastal elite, to believing that government regulation is always wrong, and that any attempt to tax the wealthiest people is immoral. Those who deviate are rapidly branded foreign, socialist or otherwise un-American.

Some wonder if it was fear of this ultra-conservative catechism that pushed a series of Republican heavyweights to sit out 2012. "The talent pool got constricted," says David Frum, the former George W Bush speechwriter who has been boldest in speaking out against the Foxification of his party. Fox sets a series of litmus tests that not every Republican can or wants to pass.

This affects those who run as well as those who step aside, setting the parameters within which a Republican candidate must operate. What troubles Frum is that it pushes Republicans to adopt positions that will make them far less appealing to the national electorate in November, with Romney's forced march rightward typical. Even if Romney somehow wins the nomination, he won't be "the pragmatic, problem-solving Mitt Romney" of yore, says Frum, but a new Foxified version. It was this process that led the former speechwriter to declare last year: "Republicans originally thought that Fox worked for us – and now we're discovering we work for Fox."

So far, so bad for the Republicans. Why should anyone else care? Because the Fox insistence on unbending ideological correctness turns every compromise – a necessary staple of governance – into an act of treachery. The Republican refusal, cheered on by a Fox News chorus, to raise the US debt ceiling this summer, thereby prompting the downgrading of America's credit rating, is only the most vivid example. The larger pattern is one of stubborn, forced gridlock, paralysing the republic even now, at a moment of global economic crisis.

The problem is compounded by a wilful blindness towards the facts. Ari Rabin-Havt of Media Matters says Fox has created a "post-truth politics", which is happy to ignore and distort basic empirical evidence. To take one example, Fox pundits constantly repeat that "53% of Americans pay all the tax". In fact, 53% pay all the federal income tax – but many, many more pay so-called payroll taxes. It's hard for a nation to make the right policy decisions if the public is misled on the basic facts. And misled they certainly are. A series of surveys has proven that Fox viewers are woefully ignorant of current affairs, the latest study revealing that it is actually better to consume no news than to watch Fox: you end up better informed.

The extremism, anger, paranoia and sense of victimhood that Fox incubates are all unhealthy for the United States. But it's inflicting particular damage on the Republican party, which could well lose a winnable election because of its supine relationship to a TV network. It turns out it is not liberals who should fear the Fox – it's conservatives.