The shadow chancellor insisted Labour could win a Commons majority – despite the party’s disastrous poll ratings – but admitted the price of failure would be resignation.
Asked if Mr Corbyn could “stay on”, Mr McDonnell replied: “I can’t see so. What we’d do is as the tradition, which is have an election for a new leader.”
Speaking to Alastair Campbell, in an interview for GQ magazine, he also said: “I think it is the same for my own personal position.”
“Within parliament itself there is a large number of people who are saying we’d rather have a referendum attached to any deal,” he acknowledged.
And he added: “Once we get to the stage of blocking no deal, a general election is on the table. If we can’t get that general election, the referendum becomes an option.”
The Independent revealed yesterday that Labour MPs are bombarding the party whips’ office with demands for Mr Corbyn to back a referendum first.
In the interview, Mr McDonnell also:
* Ruled out a coalition deal with the Scottish National Party, or the Liberal Democrats, if Labour falls short of a majority – insisting Mr Corbyn would put forward his programme and challenge the other parties to vote it down.
* Denied Mr Corbyn had been “dragged kicking and screaming” into supporting a Final Say public vote, saying: “He hasn’t. You’re wrong on this.”
* Argued “climate change is the big issue now”, which meant the election would be “more than a class revolution”.
* Denied Labour at Westminster was riven by splits, insisting: “I’ve never seen the parliamentary Labour Party more united in the last couple of years.”
* Described his 70-year-old leader’s fitness as “unbelievable”, saying: “He’s running every morning. Jeremy is the fittest person I know.”
On Labour’s election chances, Mr McDonnell denied the poll ratings – putting Labour in the low twenties – meant “the country has just decided Jeremy is not going to be prime minister”.
He insisted Mr Johnson “has got vulnerabilities just as much as Theresa May that we can expose and exploit in a campaign”.
“I’m not being unrealistic, but the political climate is incredibly unpredictable,” Mr McDonnell said, adding: “I think we can win a majority.”