If such a referendum were called, Mr Corbyn, who voted Remain in 2016, said: "I don't know how I am going to vote - what the options would be at that time".
In an interview with The Sunday Times, former Brexit secretary Dominic Raab - whose decision to quit the Cabinet triggered the resignation of several other government ministers - said May had allowed the United Kingdom to be "blackmailed and bullied" by the EU.
Corbyn said if May's Brexit agreement comes to Parliament in its current state the Labour Party would vote against it.
She compared the backstop to taking out an insurance policy, saying people wouldn't want the insurance company to be able to "pull the plug" and leave someone unprotected.
May added that the next seven days "are going to be critical" for successful Brexit talks, and that she will be travelling to Brussels to meet EU leaders before an emergency European Council summit on November 25.
"Politics is a tough business and I've been in it for a long time", she said.
He demanded that May's Government renegotiate the agreement, which outlines the terms of Britain's departure and future relationship with the EU. Nothing is agreed until everything is agreed.
Just one in five (21 per cent) strongly supported and a further quarter (26 per cent) somewhat supported the draft withdrawal agreement.
Ms Morton said: "I fully support the Prime Minister in all that she is doing".
When asked about how she felt personally about the comments she had heard about herself over the last few weeks, she replied: "Who are we here for?"
The prime minister also may key replacements which would stabilise her position, handing the role of work and pensions secretary to ally and remain voter Amber Rudd, who went full-force on the defensive for May, telling the BBC that any MPs thinking of submitting letters of no confidence should "think again".
A total of 48 letters are needed to trigger a party leadership election that could topple her as prime minister.
He said that if the threshold was reached would be incumbent on him to "inform and consult the leader of party" and "organise a ballot as soon as is reasonably practical".
Speaking on the Sophy Ridge on Sunday programme, the Labour leader said Mrs May's draft deal with the European Union was a "one-way agreement" where the European Union "calls all the shots".
At a hastily scrambled press briefing, Mrs May issued a stark warning: "If we do not move forward with a Brexit agreement, we can not know what will follow".
Many say the conditions under the draft agreement are worse.
He added that he had read numerous summaries and analyses.
"The former prime minister reportedly remarked in the early hours of June 24, after the Brexit vote had gone against him, 'Why should I do all the hard s***?'"
Dudley North MP Ian Austin said: "My priority is to get the best deal for Dudley so I want to see an agreement which helps local businesses and protects jobs, safeguards employment rights and the environment and has a proper plan on immigration".