Shall we cast our minds back to the more innocent era of 1992, when the presidential campaign of a young southern governor by the name of Bill Clinton was nearly derailed by claims that he’d had an extramarital affair with a former lounge singer by the name of Gennifer Flowers?

As it happens, Clinton survived that episode – he and Hillary appeared jointly on 60 Minutes, as Hillary famously explained: “You know, I’m not sitting here, some little woman standing by my man like Tammy Wynette”, but it was a close-run thing.

Now imagine that a tape emerged in which Clinton and his personal lawyer were heard discussing how best to pay the hush money that would keep Flowers silent, an undeclared payment that would be in violation of campaign finance laws. There can be no doubt: it would have destroyed Clinton as a candidate, and it would have been seized on as (further) grounds for his impeachment as president.

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Yet late on Tuesday, the lawyer for Michael Cohen – Donald Trump’s personal attorney, fixer and keeper of his secrets – released a tape in which he and Trump are heard discussing how exactly to fund the silencing of a former Playboy model, Karen McDougal. Cohen apparently wanted it be handled legally, while Trump seemingly had other ideas.

“We’ll have to pay,” Cohen says. Trump’s reply: “Pay with cash.”

Put aside the impact an equivalent revelation about Clinton would have made in 1992. Just imagine the storm this would have caused if it had come out at the time Cohen and Trump had that conversation, just two months before the 2016 election. The entire political class would have assumed it would be devastating.

And yet few would now bet on the Cohen tape story destroying Trump. Instead, they’ll guess it will dominate the news cycle for a few hours, and be ignored by Fox News before being replaced by something else. For this has become the established pattern.

Note this month’s revelations by BBC’s Panorama programme that Trump behaved like a “predator” at parties packed with teenage girls in the 1980s and 1990s. It included the testimony of Barbara Pilling, then a young model, who recalled Trump asking her age. On hearing that she was 17, Trump said: “Oh, great. So you’re not too old and not too young. That’s just great.” Pilling added that she “felt I was in the presence of a shark”. Again, imagine what similar revelations would have done to the standing of Clinton or any previous president. Yet for Trump, they made barely a dent.

The simple, stubborn fact is that nothing seems to move Trump’s core supporters away from him. His approval rating among Republicans remains sky high (though there are signs that the pool of Americans who identify as Republicans is shrinking, perhaps suggesting that it’s increasingly only Trump true believers who are proud to wear that party label). Trump’s 2016 observation that he could shoot people on Fifth Avenue and still not lose votes remains as valid as ever.

It’s one reason why Trump’s opponents ought not to invest too much hope in the special counsel Robert Mueller’s investigation into alleged collusion between Russia and the Trump campaign. Even if Mueller produces jaw-dropping evidence against Trump, the president’s base is unlikely to be impressed. For a flavour of the likely response, note Alex Jones’s latest Infowars broadcast, making the wild, evidence-free allegation that Mueller was involved in a child sex ring and fantasising about shooting Mueller. (Predictably, Facebook, which carries Infowars, said the broadcast did not breach its rules.)

We have to face the grim reality that in our post-2016 world few of the previous norms and standards apply. In Britain, too, we can see how things have changed. There was a time when a government admission that it was having to plan for the possibility that food and medicine would run out – not through natural disaster, but because of a policy it was pursuing – would have been terminal. Now it’s just another day in Brexit.

The problem seems to be that a chunk of the electorate – whether diehard Trump supporters or hardcore Brexiters – is impervious to any countervailing evidence. By that same logic, hope surely must rest with those voters who are in the great middle: quieter than the rest, perhaps, but open to persuasion and willing to be moved by demonstrable facts. Those people surely still exist.

If there were to be a second referendum on Brexit, their votes would be crucial. In the US, they will have a decisive opportunity to make their voice heard in November’s midterm elections. At that moment, they will have much more than a chance to punish Trump. They will also have it in their hands to restore a set of norms that currently lies battered and bleeding. It’s no exaggeration to say that the world is depending on them.