On Monday, high-profile Brexiteer and Conservative MP Johnson announced he was resigning from the Cabinet, following the agreement of a Brexit proposal that would see the United Kingdom retain close links to the European Union after exiting the organisation.
May met with Conservative lawmakers in a packed room at Parliament, in a bid to calm the feverish atmosphere in the deeply divided party.
European Union officials say they will respond to the proposals once they have seen details.
"The Chequers Car Crash crosses Theresa May's own red lines, it certainly fails Labour's six tests and it is a million miles away from the kind of Brexit people thought they were getting - whether they voted Leave or Remain in 2016".More news: Fortnite Season 5 starting on July 12
Just over one in five - 22% - think the likeliest outcome is that Britain remains in the European Union, while 7% say they don't know.
He said he would "stand four square behind the prime minister so that we can get through an agreement with the European Union based on what was agreed by the cabinet last week at Chequers".
He added that he would not run for the leadership of the Conservative Party in the future.
May has hung on to power longer than many expected after she lost her majority in a June 2017 snap election that she had called in hopes of strengthening her hand in Brexit talks.More news: Trump Nominates Kavanaugh to Supreme Court
But May's allies fear more resignations may follow.
"I think Dominic Raab will do a brilliant job of going in there and saying, 'This is what we want, are we going to get it and if not we have some alternatives'".
Although it has caused a headache, May was quick to capitalize on the fact that two of her biggest problems extricated themselves from her inner circle; she ceremoniously replaced Davis and Johnson with more amiable substitutes. Euroskeptic Conservative lawmaker Peter Bone said party activists felt "betrayed" by the government plan.
But leading pro-Brexit legislator Jacob Rees-Mogg said "I don't think a no-confidence vote is immediately in the offing".
May has said she will fight off any attempt to unseat her. "It is the Brexit that will deliver on the democratic decision of the British people", May told parliament.More news: Nebraska groups react to Pruitt's resignation
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