YouGov said May was still the most favoured choice for prime minister, though her 43 per cent rating is the lowest it has ever been.
It follows the Conservative leader's refusal to take part in a seven-way debate on Wednesday.
"I am also impressed by his willingness to talk about class issues", the former Democratic presidential candidate said Thursday during a United Kingdom speaking tour promoting his book.
May defended herself, saying: "I could have stayed on doing that job for another couple of years and not called an election", May told the BBC audience in York, northern England.
Pollsters, who universally got it wrong at the last election in 2015, showed support for May and the Conservatives falling after she was forced to backtrack on one of her most striking election pledges to make elderly people pay more for their social care, which opponents dubbed a "dementia tax".
"And I believe they should have a prime minister with a resolute determination to carry out their will".
The Conservatives have made an official complaint to the BBC after the debate about the "biased" audience in the leaders' debate and warned there must be no repeat when May and Corbyn appear on a Question Time special.
'There has to be no first use, there has to be a process of engagement to bring about, ultimately, global nuclear disarmament.
He said: 'If we did use it, millions are going to die.
"I'm afraid there is a lesson here about Jeremy Corbyn's psychology and his politics and his naivety, with which he approaches not just the logic of the nuclear deterrent but also the Brexit negotiations".
The Labour leader insisted he would not strike a deal with SNP leader Nicola Sturgeon and was working for a majority Labour government.
The Labour leader was challenged over his party's track record on anti-semitism under his leadership. "I want to form a Labour government with a majority to carry out this wonderful programme which can give so much hope and opportunity to so many people".
He was challenged on the Labour Party's response to antisemitism, saying an investigation into Ken Livingston, suspended over comments about the Holocaust, "may or may not continue".