The delicate dance by Kamala Harris’s presidential campaign to simultaneously show deference to Joe Biden, separate herself from his presidency and thwart his ambition to campaign for her has reached a critical juncture as the 2024 election approaches its climax.

The steps of the dance, which has been ongoing since Harris assumed the Democratic party nomination in August and involves efforts to shield the 81-year-old president’s ego and feelings, became even more leaden overnight on Tuesday after Biden appeared to call supporters of Donald Trump “garbage”.

Though he clarified that he didn’t mean Trump supporters but rather their attitude towards Latinos (the official transcript had Biden saying, “The only garbage I see floating out there is his supporter’s – his – his – his demonization of Latinos is unconscionable, and it’s un-American”), the comment nevertheless set off echoes of Hillary Clinton’s infamous “basket of deplorables” put-down of a section of Trump’s supporters in 2016.

In doing so, it threatened to at least partly undo the Republican campaign’s self-inflicted damage caused by a guest at the Trump rally on Sunday who described Puerto Rico as a “floating island of garbage”, as well as a string of racist remarks about Latinos, Black people and Jews.

Trump’s campaign immediately sought to distance itself from Tony Hinchcliffe’s remarks and to repair any loss of support in the critical 222 Corridor in Pennsylvania, which gets its name from route 222. For the Latino community, it is more than that. The regions of Easton, Bethlehem, Allentown, Lancaster, Lebanon, York, Harrisburg and Gettysburg and its surroundings are home to more than 50% of the state’s total Latino population.

Trump implausibly claimed to the Fox News primetime anchor Sean Hannity that he had “no idea” who Hinchcliffe was (“Somebody said there was a comedian that joked about Puerto Rico or something”), despite the fact he was booked at Trump’s signature rally, that Hinchcliffe’s podcast Kill Tony has a huge fanbase among Trump supporters, and that the rally organizers admitted they vetted each of the guests’ speeches.

But Biden’s latest incident of apparently misspeaking – last week he said of Trump, “We got to lock him up,” before immediately adding, “Politically lock him up” – may seal the deal when it comes to Harris’s willingness to allow Biden to campaign for her.

Harris found herself having to address the latest gaffe on the the tarmac at Joint Base Andrews on Wednesday, where she noted that Biden had “clarified his comments”, and added: “I strongly disagree with any criticism of people based on who they voted for.” Asked if the incident could increase the country’s political divisiveness ahead of the elections, Harris said: “I’ve been very clear with the American public – I respect the challenges that people face, I respect the fact that we all have so much more in common than what separates us.”

While Biden’s offers to join her, Axios reported, have for some time met with: “We’ll get back to you,” the veteran Democrat strategist Hank Sheinkopf said it was now almost certain that Harris will aim not to be seen with Biden at all.

“Let him be president but keep him away from the campaign, because if he shows up it gives Trump a new target to take attention away from Harris,” he said. “So long as people focus on Harris, they won’t remember Biden, and Trump won’t be able to bring the two together as the Biden-Harris administration.”

In public comments, Harris has sought to defend her record as his vice-president, but also to separate herself from Biden – whose approval rating stands at 39%, the lowest of the past seven US presidents at the end of their terms – in order to present herself as a candidate of change who will “turn the page”, not just on the Trump era but on the Biden one as well.

Harris aides have likened the Biden-Harris relationship to a slow-moving breakup, according to Axios, which quoted an aide as saying: “He’s a reminder of the last four years, not the new way forward.”

Biden’s team have not taken the hint. Biden aides reportedly still believe “Scranton Joe” could still help Harris with white, working-class voters in the Rust belt – and caught her campaign by surprise when they scheduled a Biden campaign stop in Pittsburgh over the weekend. Axios quoted a source saying: “They’re too much in their feelings” – and indeed the former House speaker Nancy Pelosi, a key figure in Biden’s dramatic withdrawal from a second term bid in July, recently confirmed to the Guardian she had not spoken to him since.

The dynamic of president and vice-president is not set. Al Gore refused to let Bill Clinton campaign for him in 2000, a decision widely viewed as detrimental to Gore’s campaign: he narrowly lost to George W Bush. And the Bush campaign strategist Karl Rove predicted back in September that it was “highly unlikely” Biden would make campaign appearances for Harris, predicting they would let him out on the campaign trail so that his feelings don’t get hurt, but that the approach would be: “Let’s get it done and get it out of the way so we can say we’ve done it.”

That deference may now be exhausted. “Vice-President Harris is grateful for President Biden’s support and appreciates that he is campaigning for her,” the Harris campaign spokesperson Ian Sams told the New York Times on Wednesday. It felt like cool understatement.

“When Biden shows up it creates chaos for her,” said Sheinkopf. “She has to be focused on herself and the electorate focused on her.” Keeping Biden as far away from Harris as possible is, he says, “critically important as this comes to an end”.