I have great respect for women. Nobody has more respect for women than I do.” So said Donald Trump during Sunday night’s debate. But if there is anything Trump proved during the debate, it’s that he just doesn’t get it. And it is going to cost him the election.

A new poll from NBC and The Wall Street Journal, taken before the debate but after last Friday’s release of a tape of Trump boasting about his ability to kiss and grope women with impunity because he is famous, shows Hillary Clinton stretching her lead to double digits.

Although results for that poll by gender have not been released, in the latest NBC/Survey Monkey poll, 63 per cent of voters said they do not believe Trump respects women, up from 55 per cent before the release of the tape — a view that was shared by 55 per cent of men and 69 per cent of women. And in CNN’s flash poll of the debate, men thought Clinton won by 49-38 per cent. But women thought Clinton won by 64-30 per cent. Given what happened, that was entirely predictable.

The tape might have been a fatal blow to Trump’s campaign no matter what. But in everything he has said since, and during the debate in particular, he sent a very clear message to women: he neither understands nor particularly cares about the kind of predation they have to endure from men such as him. Not only that, everything about the way he interacted with Clinton during the debate — interrupting her, coming up behind her to loom over her with his considerable bulk while she was talking, promising to throw her in jail if he is elected — reinforced the idea that Trump is someone who treats women with contempt.

If you listen to Trump himself and the surrogates his campaign has sent out since Friday, this is their response to the video: first, Trump didn’t mean what he said. Second, it is no big deal, just “locker-room talk” of the kind that all men engage in when they are in situations where no women are present. And third, other men, particularly Bill Clinton, have done worse.

We have to look at this argument closely, particularly what it does not contain, to understand just how much Trump is repelling women voters who are not already on his side.

The most important thing about Trump’s defence is that it never acknowledges the awful reality of unwanted sexual advances that women face every day. His words of regret have been offered only in the most general terms, so you cannot even tell what exactly he is apologising for. By now he should understand that there is virtually no woman who has not been grabbed, groped or fondled by an acquaintance, a co-worker, a boss, a relative or a stranger, always with the assumption on the attacker’s part that there is nothing she can do to stop him. Her body can be seized and violated by any man she passes on the street or stands next to at the bus stop.

On the tape, this is exactly what Trump says he does: impose himself sexually on unsuspecting women. “I just start kissing them,” he said. “I don’t even wait. And when you’re a star, they let you do it. You can do anything. Grab ‘em by the p***y. You can do anything.”

In the debate, Trump had the opportunity to show that he understands why that was so horrifying. Instead, he characterised it as no big deal. Early on, Anderson Cooper accurately described what Trump said on the tape: “You described kissing women without consent, grabbing their genitals. That is sexual assault. You bragged that you have sexually assaulted women. Do you understand that?” Trump denied it: “No, I didn’t say that at all. I don’t think you understood what was — this was locker-room talk. I’m not proud of it. I apologised to my family. I apologised to the American people. Certainly, I’m not proud of it. But this is locker-room talk.”

So what exactly was Trump apologising for? If he does not think that kissing a woman without her consent or grabbing her genitals is sexual assault, what does he think it is? Maybe he thinks it is just flirting. And maybe what he is apologising for is using salty language. It’s hard to tell.

So what might he have said? How about something like this: “I’ve had some time to think about this, and I’ve spoken about it with the women in my life. I wish I could say I always understood what it’s like to be a woman who has to constantly worry about being grabbed or kissed against her will. But I get it now. We all have a responsibility to change that reality — it’s not just up to women to speak up about their own experiences, but men have to talk to each other and to their sons about what it means to treat other people with respect.”

You are not going to hear anything like that from Trump. In his original scripted video apology, he said: “Anyone who knows me knows these words don’t reflect who I am.”

But how true is that? Here are some other stories we have heard about during this campaign:

• Temple Taggart, a contestant in the Miss USA Pageant, said that upon meeting Trump, “he kissed me directly on the lips. I thought, ‘Oh my God, gross.’ He was married to Marla Maples at the time. I think there were a few other girls that he kissed on the mouth. I was like, ‘Wow, that’s inappropriate’”

• Jill Harth, a pageant owner who with her longtime boyfriend had business dealings with Trump, says that Trump put his hands on her thigh and genitals during a dinner, proclaimed his sexual attraction to her in front of her boyfriend, and during a visit to Mar-a-Lago brought her into Ivanka’s bedroom, where “I was admiring the decoration, and next thing I know he’s pushing me against a wall and has his hands all over me”

• Multiple employees at Trump’s golf course in California told the Los Angeles Times that he would insist that female employees he found insufficiently attractive be fired

• He pressured his then-girlfriend Marla Maples to pose nude for Playboy. (She refused)

• On the Howard Stern show, Trump bragged that he liked to go backstage at the Miss Universe Pageant and watch the contestants undress, and no one could stop him. “I’ll go backstage and everyone’s getting dressed, and everything else, and you know, no men are anywhere, and I’m allowed to go in because I’m the owner of the pageant and therefore I’m inspecting it,” he said. “And you see these incredible-looking women, and so, I sort of get away with things like that”

• Multiple former employees on The Apprentice told the AP that Trump regularly made lewd sexual comments about female members of both the cast and crew, often with the cameras rolling. “We were in the boardroom one time figuring out who to blame for the task, and he just stopped in the middle and pointed to someone and said, ‘You’d f*** her, wouldn’t you? I’d f*** her. C’mon, wouldn’t you?’”, one person reported. “Everyone is trying to make him stop talking, and the woman is shrinking in her seat”

Perhaps you find one or another of these stories implausible. But even if you do, the volume of them should suggest to Trump that he has a particular need to reassure women that he does not think of them just as objects that he is free to manipulate, humiliate or even grope at will. Yet in the debate, he did exactly the opposite.

His response sounded like it was crafted with the help of campaign chief executive Steve Bannon, who was accused by his ex-wife of domestic violence, Rudy Giuliani, who sadistically humiliated his second wife while having an affair, and Roger Ailes, who is accused of sexual harassment by dozens of women. Given that brains trust, it is no surprise that when he has a chance to repair the damage, he only makes things worse.

I have been saying for a long time that the gender gap in this election could be the biggest in history, and at this point that appears to be a near-certainty. If Trump does not change how women voters think of him, he cannot win, period. But he doesn’t even seem to understand why they are so disgusted by him — or if he does understand, he is simply incapable of showing them that he is the person he claims to be.

•Paul Waldman is a contributor to The Plum Line blog, and a senior writer at The American Prospect