Crude and crass, this tape has enough political dynamite to destroy his faltering campaign. "This one will cause real damage," Republican pollster Frank Luntz said.

And it confirms the darkest fears of so many in the GOP who opposed his nomination – if a party is reckless enough to run a candidate as dangerous as Trump, it has only itself to blame when cast-iron evidence surfaces of him being his worst self. That he did it in the company of a scion of a revered GOP family – the Bushes – only makes it worse.

The vulgarity is bad enough. Worse is Trump's presumption that men are entitled to treat women purely as sex objects - "when you're a star, they let you do it".

And his initial response to its publication byThe Washington Post – just "locker-room banter" – is a poor attempt to normalise what for many veers towards criminal conduct.

Dawn Laguens, executive vice president of Planned Parenthood Action Fund, predicted the video would sink Trump's candidacy.

"If someone, quote, 'grabbed someone by the p---y', to quote Donald Trump, on a subway or on a bus or at a school, they would be in jail. They would be arrested and prosecuted, and they would go to jail," Laguens told The Post. "I think we are now moving to the end of the end of Donald Trump."

Jeb Bush tweeted his outrage: "As the grandfather of two precious girls, I find that no apology can excuse away Donald Trump's reprehensible comments degrading women".

And the GOP's 2012 candidate and vocal Trump critic Mitt Romney was not far behind:

Trump fired off a statement on Friday afternoon, claiming he was sorry if his language offended anyone.

"This was locker-room banter, a private conversation that took place many years ago. Bill Clinton has said far worse to me on the golf course - not even close… "

But Hillary Clinton, wife of the former president and Trump's Democratic rival for the presidency, struck back, tweeting: "This is horrific. We cannot allow this man to become president".

The video is all the more damaging for Trump and embarrassing for the Republican Party because much of his demeaning of women has come in the form of insults that were not explicitly sexual, and explicit accounts by women of his offensive conduct, inevitably, have been cast in a she-said-he-said vein.

"No woman should ever be described in these terms or talked about in this manner. Ever," said Republican National Committee Chairman Reince Priebus in a statement, according to the Washington Post, a rare condemnation from the party's chairman who has stood by Trump through several other controversies.

The crisis amounts to a critical challenge for senior republicans, not to mention Trump's running mate and Indiana Governor Mike Pence who was shielded from reporters as the story broke, to end the ambivalence by which they criticise Trump's serial excesses, but continue to promote and him as a fit and proper Republican candidate.

House Speaker Paul Ryan said he was "sickened" by the comments and said he would no longer appear with him at a campaign event in Wisconsin on Saturday.

"This is the moment candidates should cut ties with Trump," said Mike Murphy, a Republican strategist, adding pressure on Ryan before he cancelled the appearance: "I recommend Paul come down with a dental emergency tonight."

Republican Senator Kelly Ayotte, of New Hampshire, who last week tried to walk back her observation that Trump was a role model, is one of the two-timers, continuing to endorse Trump, but saying in a statement: "His comments are totally inappropriate and offensive".

Challenging Ayotte in the November election, New Hampshire Governor Maggie Hassan hit out: "These vile comments from Donald Trump cannot be excused. It is beyond comprehension how Senator Ayotte could continue to support this man for the highest office in the land, let alone call him a role model."

The pressure on Trump's key backers was evident, but one of his most high-profile social-conservative supporters, Tony Perkins of the Family Research Council made quite clear that his support was purely political, not values-based. He told BuzzFeed: "My personal support for Donald Trump has never been based upon shared values."

Trump's derogatory and lewd comments about women have been under constant attack in the campaign – and not only by Democrats. He has responded by raising Bill Clinton's philandering – and accusing Hillary Clinton of being "an enabler".

Interviewed on a Las Vegas television station on Wednesday, Trump claimed his comments about women, some cast in vile terms, had been made for "entertainment".

"A lot of that was done for the purpose of entertainment. There's nobody that has more respect for women than I do," he said in the interview.

"Are you trying to tone it down now?" asked the interviewer, Jim Snyder.

"It's not a question of trying, it's very easy," Trump assured him.

Predating the hugely successful, campus-based "yes, means yes" campaign against sexual assault, the 2005 encounter took place when sexual assault was described legally as "the carnal knowledge of a female, forcibly and against her will".

In 2012, it was amended to mean "the penetration, no matter how slight, of the vagina or anus with any body part or object, or oral penetration by a sex organ of another person, without the consent of the victim."

The Justice Department now describes sexual assault as "any type of sexual contact or behaviour that occurs without the explicit consent of the recipient". Presumably that would include grabbing an unsuspecting woman "by the pussy".

"That's nothing less than someone talking about committing sexual violence - the kissing, the grabbing," Bridgette Stumpf, co-executive director of legal services at the Network for Victim Recovery, told The Washington Post.

"He's talking about women as if they're objects, as if they don't have a right to consent to the way someone touches them. This is how sexual violence becomes accepted in our culture." She later tagged one of her tweets with the hashtag #rapeculture.