Labour leader Jeremy Corbyn said Mrs May should make way for a Labour administration if her Government can not get its act together quickly.
Foreign Secretary Boris Johnson and Brexit minister David Davis quit government in protest at May's plan for Brexit, which she had agreed with her cabinet last Friday, throwing her government into chaos.
Mrs May appointed junior minister Dominic Raab, a former diplomat who was a prominent campaigner for Leave in the 2016 referendum, as Mr Davis's successor.
Leaving Chequers on Friday night the Prime Minister could be forgiven for thinking she had gotten away with it, albeit by the skin of her teeth.
Last Friday at the prime minister's country retreat at Chequers My May brokered a "collective" agreement on proposals for the future relationship between the European Union and UK.
May replaced Johnson at the foreign office with Jeremy Hunt.
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District Court in Pittsburgh in 2003. "Republicans are holding four lottery tickets, and all of them are winners", said Sen. A fellow judge there, Maryanne Trump Barry, one of the president's sisters, reportedly has recommended him to her brother.
Davis quit late Sunday saying he could not support May's plans for close trade and regulatory ties with the bloc after the United Kingdom leaves the European Union next year.
Mrs May later faced down backbench critics at a meeting of the 1922 committee, amid rumours they were close to getting the 48 signatures needed to trigger a no-confidence vote that could spark a leadership election. They have organised a highly successful Commonwealth summit and secured record global support for this Government's campaign for 12 years of quality education for every girl, and much more besides.
Mrs May came under fire from Jeremy Corbyn, leader of the opposition Labour Party, who said she "has no authority left and is incapable of delivering Brexit".
Tory digital minister Matt Hancock - known for his self-branded social networking app - will now takeover Hunt's portfolio as Health Secretary.
The European Commission declined to comment on Mr Davis's exit but Donald Tusk, the president of the European Council, said he hoped a change in faces might lead to a change in policy.
Meanwhile, the pound fell against the dollar and the euro following Mr Johnson's resignation, with analysts warning it was likely to fall further if he launched a leadership challenge to Mrs May. He pointed out that while some Brexiteers want to leave the customs union and single market, others advocating for a so-called "soft Brexit" want to stay.
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