"Well done to Jo Johnson for joining the ranks of those who think we can do better".
Johnson said there was now a huge gulf between the type of Brexit that was promised by his brother Boris, a leading campaigner to leave the European Union, and the deal that May is hammering out in Brussels.
Sky News' political editor Faisal Islam said: "It is bad news for the Government that Jo Johnson - who was helping to organise no deal planning for the trade border - resigns in this way with an extra vote against the withdrawal agreement".
Joseph Johnson believes that Britain is on the verge of severe crisis since the Second world war and assured the loyalty of the Conservative party, despite the resignation.
Still, if the four ministers indeed quit the May cabinet - just days after Jo Johnson's resignation - such a move could spark a legitimacy crisis in the British government.
A spokesperson for May's office said later Friday that under no circumstances would a second referendum be held.
Despite their difference in stance, he said they were "united in dismay" at the "intellectually and politically indefensible" UK position.
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He acknowledged that a no-deal Brexit could result in "Kent becoming the Lorry Park of England", with real questions about guaranteeing supplies of food and medicines.
He added: "In the sense that if you betray the British people where they no longer believe in democracy... you don't know what the consequences are".
"It does not remotely correspond to the mandate of the people in June 2016".
Jo Johnson's resignation, and his call for a fresh referendum to test voter sentiment, further complicates matters for May as she tries to strike a deal with European Union leaders that would pass muster with her own cabinet and win backing in Parliament.
He told the BBC: "When we get the final deal, and it feels like that's not very far away, Cabinet ministers will have to look into their hearts and see whether or not they feel they can support it".
People's Vote campaigners think the most realistic route to another referendum is that parliament votes down May's deal and the opposition Labour Party fails to trigger a general election. There are several sticking points, however, most notably the status of the border between Northern Ireland, a United Kingdom territory, and the Republic of Ireland.
DUP leader Arlene Foster said the Prime Minister appeared "wedded to the idea of a border down the Irish Sea" despite Downing Street's repeated assurances to the contrary.