Mr Biden made the remark after President Trump accused him of having an “anti-vaccine rhetoric”. On Monday, Mr Trump said Mr Biden and his running mate Kamala Harris needed to “immediately apologise for the reckless anti-vaccine rhetoric”.
Mr Biden responded to the accusation during a campaign trip to Lancaster and Harrisburg, Pennsylvania.
He said: “If I could get a vaccine tomorrow, I’d do it.
“If it would cost me the election, I’d do it.
“We need a vaccine and we need it now. As quickly as we can get it.”
Ms Harris said over the weekend she feared Mr Trump might fast-track the development of a vaccine in order to boost his popularity during the election, arguing that doing so could jeopardise the safety of the vaccine.
Speaking to CNNC, she said: “I will say that I would not trust Donald Trump and it would have to be a credible source of information that talks about the efficacy and the reliability of whatever he’s talking about.
She added: “I will not take his word for it.”
The California senator also suggested members of the medical community could potentially be censored.
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As well as the tweet, Mr Biden posted a link to his official website where he outlines how he would reopen schools.
He wrote: “The challenge facing our schools is unprecedented.
“President Trump has made it much worse.
“We had a window to get this right. And, Trump blew it.
“His administration failed to heed the experts and take the steps required to reduce infections in our communities.
“As a result, cases have exploded.
“Now our window before the new school year is closing rapidly, and we are forced to grapple with reopening our schools in an environment of much greater risk to educators, students, and their families than there would have been if America had competent leadership.”
In his push to reopen schools full last month, Mr Trump branded as “a little ridiculous” some school districts’ plans to reopen par-time.
The move involved pupils attending in person some days and online on other days in order to allow enough room for social distancing.
But labelling coronavirus as “the China plague”, Mr Trump said: “One thing we’ve learned during this horror show of the China plague is that virtual is not as good as being there.”