Mr Corbyn has already made clear he would support a fresh public poll if his party could not secure its preferred Brexit deal.
The concerns were aired on the Sky News show Sophy Ridge on Sunday which came to the town to shine a spotlight on a parliamentary seat that often reflects the national outcome in a general election.
Ministers have also openly flouted collective cabinet responsibility to vote against her.
Theresa May will have to promise to make a "dignified departure" from Downing Street to get her deal through, a former Cabinet minister said last night. But what I do know is we as a party want to be able to thank her.
"If people felt I could and they wanted to back me I would", the former work and pensions secretary said on Sunday.
"We either vote for this bad deal or get no Brexit which would fly in the face of democracy", she tweeted.
She said Mrs May's Cabinet was "making her position very dubious".
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She added that, if enough people asked her to stand, she would put herself forward in the next leadership contest.
But while they're ready for a general election at any time, the town's Labour MP believes that is not possible until a Brexit deal is agreed by the House of Commons.
"We are not just going to keep presenting it if we haven't moved the dial".
He added: "I would say to my colleagues: all actions have consequences, and if you really want to deliver the Brexit we all promised... if we actually want to do that then we need to back the Prime Minister's deal because there is no other deal on offer".
During their meeting, if MPs reject again the withdrawal agreement struck in November by Mrs May and Brussels, the EU37 will have to discuss whether or not to concede an extension to Article 50 to the United Kingdom, as asked by Parliament with a vote held last Thursday.
Mr Elphicke, a member of the hardline European Research Group, said: 'What I am clear on is that if we are going to support it, there needs to be a change of negotiating team for the future relationship because there's no way to be carrying on with Parliament.