Conservative whips, who enforce discipline in the party, threatened to call a confidence vote that could bring down the government before a crucial vote on Tuesday on customs, one lawmaker told Reuters.
While praising May's "courage and resilience", Johnson said her Chequers plan would see the United Kingdom in "miserable limbo".
But having trusted the Prime Minister to deliver on her "Brexit means Brexit" promise, he now finds her latest proposals unacceptable.
The prospect of continued drama in parliament and doubts over the future of May's "white paper" Brexit plan-which is itself only a starting point for talks with the European Union - is testing the patience of businesses that depend on cross-border trade.
Maurizio Sarri set to be joined by Jorginho at Chelsea
Sarri has been lined up to replace his compatriot and is determined to bring Jorginho with him as Chelsea plot a £57m double deal. John Terry , who left Chelsea after 22 years last summer following one campaign under Conte, paid tribute to the Italian.
Mr Baker, rising to huge cheers from Tory backbenchers, said: "It is in the national interest that we should have and have implemented contingency plans for the unwanted eventuality of exiting the European Union with nothing agreed".
But the pro-EU lawmakers lost Tuesday by six votes - 307 to 301.
Mr Johnson praised the "great clarity" of Mrs May's speech at Lancaster House, where she said Britain would leave the customs union and single market but strike new trade deals with the EU and countries worldwide.
Explaining that the two states already have the same rules and laws, the Tory MP told the BBC: "The only reason we wouldn't come to a free and open agreement is because politics gets in the way of economics".
Afterwards, Mrs May announced she will go on a summer tour to try to sell her Brexit plan among seething Tory activists who have slammed it.
The original Chequers agreement caused the resignations of Davis and Johnson.
Colbert says Trump's meeting with Putin should count as 'treason'
We are past the point where Trump's conduct can be ascribed to his belief that it is imperative to improve US-Russia relations. Putin declined but, according to the Post , he did send "a "friendly" letter and a gift of a Russian lacquered box" to Trump.
And Wes Streeting, a supporter of the People's Vote campaign for a second referendum, said: "Boris Johnson's speech was a total damp squib". It was not the plan agreed by the government earlier this month at May's country retreat at Chequers, he said.
"It is absolute nonsense to imagine, as I fear some of my colleagues do, that we can somehow afford to make a botched treaty now and then break and reset the bone later on", said Johnson.
The dispute has exposed the deep divisions in May's party and could yet lead to significant challenges to her authority.
The close shave was May's third this week as she presents legislation on one of the most important and divisive decisions in modern British history with only a minority government, and a Conservative party at war with itself.
In his letter, Mr Davies continued: "Failure to keep our promise to the electorate will nearly certainly lead to the catastrophe of Jeremy Corbyn becoming Prime Minister and I can not sit back and allow that to happen".
Motorcyclist’s leg severed after struck on Kansas City highway
The suspect was considered a person of interest in the slaying of college student Sharath Koppu in Kansas City earlier this month. Police have taken the vehicle and placed in custody the other person, who is believed to be not involved in the fatal robbery.