An influential Labour donor called on the leftie boss to work with Theresa May to ditch her withdrawal agreement and push for a genuine free-trade deal.
And Mr Corbyn was warned that adding his voice to the push for a second EU referendum "would be a death sentence for Labour".
Labour are under pressure to switch their policy and start supporting a rerun of the 2016 vote.
Mr Corbyn has been lobbied by the Shadow Cabinet to back a second referendum if the PM's Brexit deal falls next week.
But Brendan Chilton, who runs Labour Leave, today warned that a U-turn would drive away millions of Brexit-backing Labour voters.
He stormed: "If Labour goes down the route of supporting a second referendum, we will cease to be able to call ourselves the Labour party.
"We'll probably be decimated in our heartland seats. You'll have the Tory party or something else representing proper Labour territory.
"Clearly Jeremy is struggling at the moment because you've got individuals within the Shadow Cabinet and within the parliamentary who are very much Remain.
"They want to have a second referendum and keep us in the European Union – that would be a death sentence for Labour outside London and metropolitan areas, and we just simply can't allow it."
John Mills, who has donated huge sums of money to Labour, added that Mr Corbyn should support plans for a "Canada-plus" free-trade agreement to replace Mrs May's deal.
He suggested that Labour could lose dozens of Commons seats if it alienates Leave voters.
Mr Chilton told The Sun Mr Corbyn should be true to his Eurosceptic principles.
He said: "We all know Jeremy's a Brexiteer and if he wasn't leader of the Labour party right now he's be on the back benches, attacking this deal and saying we need to get out as quickly as possible. We know where his heart truly is."
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