Trump and Vance’s Springfield smear is a microcosm of their entire campaign | Sidney Blumenthal

After Donald Trump's disastrous debate with Kamala Harris on 10 September he decided to center his campaign on a single incendiary issue: "In Springfield, they're eating the dogs. The people that came in, they're eating the cats. They're eating the pets of the people that live there."

When Trump was corrected during the debate by the ABC moderator David Muir, who pointed out that his statement about the Haitian community in the Ohio town was erroneous, he insisted it was factual. "Well," he said, "I've seen people on television, people on television say, 'My dog was taken and used for food.'" But there were no such "people on television". There were no dogs taken for food. Trump called Muir a "foolish fool", and said, "He's a guy with good hair, but not as good as it was five years ago."

Trump showed up at the debate with a new hairstyle and tint - less Liberace and brassy blond, cut a bit shorter and softer, and shaped without the stiff angular pompadour - to lend him a more youthful appearance. His hair is always a preoccupation that has in the past had priority over policy. On a visit to France, in 2018, he refused to attend a memorial service at the Aisne-Marne American cemetery of first world war soldiers near Paris in a light rain whose humidity might loosen the firm hold of his hairspray, and gave as an excuse that the fallen were "suckers" and "losers".

At the debate, he was anxiously competing with someone on the stage other than Kamala Harris. He was fixated on the hair of the younger male journalist. His narcissism exhausts him. It gives him no rest. "It was three against one," Trump said. "I was surprised at David Muir. I thought he was a high-quality person, but he is just a sleaze like the rest of them."

But Trump quickly gave up on Muir's hair to focus on the more significant issue of "eating the pets". Trump's obsession was not an absurd, spasmodic or random act. It was not an off-ramp along the winding road of his incoherent digressions. Trump homed in on the lie as a strategic necessity. Trump understood that its outrageousness would make it unforgettable and repeatable. The falsehood served to personify the fears he routinely seeks to arouse of an alien invasion. The dogs and cats substitute for his usual horror story about a young woman murdered by an immigrant in the country illegally. He moved the blood libel to lovable pets.

After the debate left him staggering into the spin room to proclaim, "It's the best debate I ever had," before confusedly retreating, Trump's imperative has been to hold on to his base. He can afford no erosion. Losing even a point might be a falling rock that starts a landslide.

Trump desperately needed to distract the national discussion away from abortion. His pre-debate charade of gyrating positions failed to beguile women voters. His charm offensive was offensive without the charm. The gender gap widened to an even greater chasm.