The British government says Foreign Secretary Boris Johnson has resigned, amid a widening split in the Cabinet over Brexit.
May met with Conservative lawmakers in a packed room at Parliament, in a bid to calm the feverish atmosphere in the deeply divided party.
"I would be surprised if one [a leadership contest] is precipitated and if there is, I suspect she'd win it", he said.
"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".
Mr Davis was the first to go, followed by Mr Baker, with Mr Johnson resigning in the afternoon, then Mr Green, and then finally Mr Burns.
When asked whether May would contest any vote on a confidence motion in her leadership, her spokesman said: "Yes".
"That dream is dying, suffocated by needless self-doubt".
"My concern is about the policy rather than the individual", he said.
Judge Extends Deadline for Reuniting Migrant Children Sabraw has also ordered the government to reunite almost 3,000 children five and older with their parents by July 26. The government has said only 3 of the children had accompanying adults that were found to not be their parents.
The plan agreed at May´s country retreat at Chequers would involve Britain pursuing a "UK-EU free trade area" for goods that would involve regulatory alignment with the EU.
Another said the second resignation made the looming October deadline highly unlikely as Mrs May attempts to rebuild her Cabinet.
The Sun, Britain's biggest-selling newspaper, said there had been "blunder after blunder" by May.
Government unity began to fray within hours. Brexit-supporting lawmakers were angered by the proposals, saying they would keep Britain tethered to the bloc and unable to change its rules to strike new trade deals around the world.
That makes negotiating a deal with the European Union very hard: The bloc has said that Britain can't pick and choose the "four freedoms" (free movement of goods, capital, services, and people) and have an "a la carte" Brexit.
After Mr Davis' resignation, European Union diplomats laughed off any possible effects on the Brexit negotiations, insisting the Prime Minister's European Union sherpa Olly Robbins is the UK's main man in Brussels these days.
Newly appointed Brexit secretary Dominic Raab.
In this video grab taken from footage broadcast by the U.K. Parliamentary Recording Unit (PRU) via the Parliament TV website on July 2, 2018, leader of the opposition Labour Party, Jeremy Corbyn listens as Britain's Prime Minister Theresa May answers questions after making a statement in the House of Commons on the European Union summit and Brexit developments.