Many politicians are unhappy with her compromise plans to maintain the free trade of goods with the European Union, which they say will leave Britain subject to decisions in Brussels without any input.
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.
This is despite the fact he reportedly wrote the 2015 election manifesto for the Tory party promising to "honour the result of the  referendum, whatever the outcome".
Johnson - who had backed staying in the bloc in the 2016 referendum - is the younger brother of Boris Johnson, who spearheaded the pro-Brexit campaign and quit as foreign secretary in July over May's Brexit blueprint.
"It has become increasingly clear to me that the withdrawal agreement, which is being finalised in Brussels and Whitehall even as I write, will be a awful mistake", said Johnson, who was a transport minister in the government.
Jenny Chapman, Shadow Brexit Minister, said: "Jo Johnson is the eighteenth minister to resign from Theresa May's government".
If a deal is voted down by parliament, the country could be thrust into an uncertain future. Theresa May has said the withdrawal deal was 95 percent done - but there was no agreement yet on how to guarantee no hard border in Northern Ireland.
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He started off his exchange with the president by saying that he will "challenge" Trump on his description of the migrant caravan. Trump said he hadn't made a decision when asked by a reporter how long Acosta would remain in the "penalty box".
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. Meanwhile, a spokesman for May's office says there will not be a second referendum on Brexit under any circumstances.
They also suggested he had been privately supporting the work of anti-Brexit campaign group, People's Vote, "for some time" despite being a government minister. I reject this false choice between the PM's deal and "no deal" chaos.
It added: "The prime minister thanks Jo Johnson for his work in government".
He denied his actions amounted to a coup against the prime minister.
Clive Lewis, a Corbynite MP who left the shadow cabinet to vote against triggering Article 50, highlighted Johnson's criticism of the Tory Brexit plan.
The Northern Irish DUP - who May relies on for her parliamentary majority - has criticised the government's proposed plan, saying it could allow Northern Ireland to be separated from the UK.
Speaking of his brother, Jo Johnson acknowledged that the Brexit negotiations "have at least united us in fraternal dismay".