A special US election poll compiled for The Independent by JL Partners found a majority of Americans, 51 per cent, said they would be confident while taking a coronavirus vaccine. But among Mr Trump's supporters, that figure drops under a scenario in which Mr Fauci endorses a vaccine.
Fifty-four per cent of the president's backers express confidence in a vaccine before a Fauci endorsement is mentioned.
But after, that figure drops to 45 per cent.
Mr Trump and Mr Fauci have traded barbs, again, over the last few days.
The president called the scientist a "disaster" on a Monday call with campaign staffers, declaring Americans "tired" of hearing about Covid-19. He also alleged, without supporting evidence, that had Mr Fauci, not him, been in charge of the federal response, half a million Americans would be dead.
The president attacked Dr Fauci on a campaign call to staffers and said that if the scientist had been in charge more than 500,000 Americans would have died.
"Fauci is a disaster. If I listened to him, we'd have 500,000 deaths," Mr Trump said on the call, according to CNN. "If there's a reporter on, you can have it just the way I said it, I couldn't care less."
The senior National Institutes of Health official got the first word, criticizing the president for a so-called "superspreader" event earlier this month at the White House to honour Supreme Court nominee Amy Coney Barrett.
Mr Fauci said he is "absolutely not" surprised the commander-in-chief fell ill after the event, where few attendees wore masks or followed social distancing guidelines during indoor and outdoor ceremonies.
"When I saw that on TV, I said, 'Oh my goodness. Nothing good can come out of that, that's got to be a problem.' And then sure enough, it turned out to be a superspreader event," Mr Fauci said on CBS News' "60 Minutes" program.
Despite the war of words, Mr Fauci and Mr Trump share a defensive posture about how the federal government has handled the pandemic.
"I don't think," he told CBS, "we could have possibly have done any more than that."
JL Partners were commissioned to poll American voters on behalf of The Independent and spoke to 1,034 respondents across the U.S.
A slim majority of voters said they would be confident to take a Covid vaccine with 51% saying they would be very confident, 8 % neutral and 41 % either not very confident or not confident at all.