An unseemly feud has erupted in the Republican realm, between the party's most-influential news network and its poll-leader in the U.S. presidential primary.

It's Fox News vs. Donald Trump.

The spat ignited during this week's ratings-record-smashing primary debate, where the bombastic billionaire felt he was unfairly targeted by the Fox crew.

Trump responded in characteristic fashion — with an escalated attack against the network, and with a particularly crude reference to one of the debate co-moderators, Megyn Kelly.

He did it during an appearance on rival network CNN.

"I'm very disappointed in Fox News," he told CNN on Friday. "I think they probably had an agenda. But, certainly, I don't have a lot of respect for Megyn Kelly ... She gets out, and she starts asking me all sorts of ridiculous questions. And you know, you can see there was blood coming out of her eyes, blood coming out of her wherever."

It was that last phrase — "blood coming out of her wherever" — that had some conservatives saying he'd finally taken his mean, often-misogynistic shtick too far.

Trump backtracked on Saturday, attempting to explain that his quote referred not to menstruation but to a nose bleed.

He was nevertheless booted out of a planned Republican grassroots event Saturday. Kelly was invited in his stead.

A rival presidential candidate, former Hewlett-Packard CEO Carly Fiorina, joined in the chorus of criticism of the reality TV star.

The event from which Trump was uninvited was the RedState Gathering, a two-day forum for GOP candidates and leading conservative voices.

Erick Erickson, a writer at and a Fox News contributor, made the decision to uninvite Trump and criticized the candidate on Twitter, saying. "It is a shame that a candidate for president confuses political correctness and common decency."

Erickson has himself landed in hot water for comments made about women, having tweeted in 2013: "I am proud of myself for pointing out to the Women & Gender Studies students that their major has no real world value."

The debate brought to the surface a tension that's bubbled within the party, amid Trump's meteoric rise to the top of the Republican primary polls.

That tension was hinted at weeks ago when Fox owner Rupert Murdoch suggested Trump was embarrassing his party. However, the media mogul had tamped down his criticism as the Republican establishment wrestled with how to defuse the human grenade in their midst.

Trump has flirted with the idea of a third-party run that would split the right-wing vote and potentially blow up its prospects of defeating the Democrats next year.

So most of the field, and the conservative commentariat, has been handling him with care — cringing silently through every outrage to avoid poking the man a rival campaign likened to a rattlesnake.

But that appeared to change in Thursday's debate, which attracted an audience of 24 million, which was by far the largest in the history of U.S. cable news.

Moderators opened the debate by quizzing Trump on a third-party run. Kelly read a list of past insults he'd levelled against women including "fat pig" and "dog." Other candidates faced tough questions but none were pressed as hard as Trump.

Once the debate was over, the network ran a focus group where participants trashed Trump's performance.

Attacks continue on Facebook

The billionaire's backers sprang to his defence, slamming the focus-group leader Frank Luntz, and unleashing a torrent of insults on Kelly's Facebook page.

Trump himself led the counter-attack. He called Luntz a slob, and tweeted at Fox News: "You should be ashamed of yourself. I got you the highest debate ratings in your history & you say nothing but bad."

Liberals leaned back and enjoyed the show.

One writer called the debate the funniest political program in American history. Matt Taibbi also called it a well-deserved reckoning for the Grand Old Party, which has fed a fear of foreigners that Trump is now exploiting.

"The Republican party and its allies at Fox, on afternoon radio and in the blogosphere have spent many years now whipping audiences into zombie-style bloodlusts," wrote the Rolling Stone writer.

"When it suited them, party insiders told voters across middle America that foreigners were trying to crawl through their windows to take their wives, and that stuffed suits in Washington and in the media were conspiring to enslave their children in Marxist bondage.

'They created this monster'

"Now all of that paranoia is backing up on them. They created this monster, and it's coming for them now. Trumpenstein lives. He is loose in the town and on his way to the doctor's castle. We may not be laughing two years from now, but for the time being, man, what a show."

Trump has a huge lead in the most recent Republican polls, although most serious pundits predict his support can't grow because too many voters dislike him.

If he runs as an independent, however, he could take a severe bite out of the Republican vote.

And because he's held some liberal positions in the past, and donated to Democrats, and because the Clintons attended his 2005 wedding, some conservatives are starting to accuse him of being a Democratic double-agent.

With files from CBC News