Tory Rory Stewart wants to ring up 50,000 people to ask them to sort out Brexit if he can’t.
The MP, who is running to be the next Prime Minister and leader of the Conservative Party, plans to launch a Citizen’s Assembly if he can’t get a deal through Parliament.
And he ruled out serving in Boris Johnson’s cabinet if his rival beats him in the Tory leadership election.
He told the BBC’s Andrew Marr: “First thing is to get Parliament to try to get Brexit through. In the end we live in a Parliamentary democracy, so we have to begin by convening Parliament.
“If I were lucky enough to be elected as leader, I would come in with a mandate from Conservative Party members, the associations in the country, and I could make a different request to Conservative members than the Prime Minister was able to, perhaps, in the past.
“And I would hope, also, that the results of the European Elections would make Members of Parliament realise that we need to get Brexit done and get that deal passed.
“But if it failed, the plan B, the fallback, would be to go to a citizens’ assembly.”
He went on: “That would be like a jury selected very scientifically across the country, whittled down to be representative of the country as a whole.
“Give them 3 weeks to go through the details of it and then make recommendations.”
He said he hoped the phone calls would go out in late July – but denied the idea was “passing the buck.”
He said: “It would work like this, you would go to select randomly from the electoral register 50,000 people. You would then…write or phone them to check who’s available.
“And then you’d use a polling company to make sure they’re representative of the country – north against south, women against men, Brexit against no-Brexit.
“And the reason to do it is to release the pressure from Parliament. Parliament is gridlocked and stuck.
“I would give Parliament another go, but I would say to Parliament: ‘This is the last chance saloon. Get it done, but if you’re not going to get it done, let us have the citizens’ assembly.’”
Mr Stewart said Boris Johnson’s plans for Brexit will come “off the rails” once it is subject to detailed examination.
And he warned that Mr Johnson’s reluctance to submit to media scrutiny was undermining trust in politics.
He said: ”How is Boris going to deliver Brexit? He keeps saying ‘I am going to deliver it’. I don’t even know what he believes. He won’t talk to me. He won’t talk to you. He won’t talk to the public.
“We want to know what he believes. The real problem with politics is a problem of trust.
“Nobody has had the chance to question him and as soon as you question him and as soon as I sit down with him and ask the big question – how, how are you going to deliver Brexit? How are you going to get a no-deal through? – Then it begins to come off the rails.
“We are a moderate country, we are not a Trumpian country,” Mr Stewart added.
And he confirmed he would not serve under Boris Johnson as Prime Minister.
“I would not serve,” he said. “I would not serve under a Boris cabinet. I’m not in this to be in the cabinet. I’m in the cabinet already. If I wanted to be in the cabinet I could just stay and keep my mouth shut. I want to change this country, and I want to challenge and say there are two completely different visions facing our country: Boris’ vision and my vision.
“His strategy on Europe and mine. His view of economics and mine. And the question is, who is going to represent us? Who do you want to represent us?”