The brother of former foreign secretary Boris Johnson, a leading Leave voice, said the practical terms of Brexit that the British government managed to get from Brussels are a far cry from what people imagined when the voted during the 2016 referendum.
Johnson said "Britain stands on the brink of the greatest crisis since the Second World War".
The deal being negotiated with Europe by the government - dubbed the "Chequers Deal" - would leave Britain economically weakened with no say in European Union rules it would have to adhere to for years, while a "no deal" scenario would inflict damage on the country. "We know a General Election is their first choice, question becomes what is their second choice - exit or referendum".
"I reject this false choice between the PM's deal and "no deal" chaos", he wrote.
On Friday the DUP, whose support Theresa May relies on for votes in the Commons, said they can not support any deal which included the possibility that Northern Ireland would be treated differently from the rest of the UK.
Asked on Friday whether an agreement could make it through Parliament, de facto deputy PM David Lidington said he hoped that if a deal is agreed between the United Kingdom and European Union it would create a "new dynamic" in Westminster.
A Downing Street spokesman said: "The referendum in 2016 was the biggest democratic exercise in this country's history".
Transport Minister Jo Johnson has stepped down to protest UK Prime Minister Theresa May's Brexit plan.
He said the public should be given the chance to vote again on whether they want Brexit, and if so whether they accept what is on offer or choose to leave without a deal.
David Lidington said a UK-EU deal would involve "compromises, give and take on all sides" but when faced with "product on the table" in the form of an agreement backed by all 28 governments there could be a shift in attitude at Westminster.
Johnson said the mooted deal had united him in "fraternal dismay" with his Brexit-backing brother Boris saying he could not support May's Chequers strategy.
But even a no-deal Brexit "may well be better than the never-ending purgatory" that Mrs May's plan would offer.
"I hope and I believe that we can secure that majority in Parliament for the agreement", he said.
His older brother Boris wrote on Twitter after the announcement: 'Boundless admiration as ever for my brother Jo.
"I think that MPs, MEPs too. will be looking at what that deal says", the Cabinet Office minister said.