Leading proponents of Brexit called on her to abandon the deal struck with the Cabinet last Friday at Chequers, her country retreat outside London.
Dominic Raab, a Brexit supporter and former housing minister, was appointed to replace Davis only days before negotiations in Brussels are due to resume next week.
"Top-level cabinet resignations usually spell trouble for a government and Boris Johnson's might well have led to a leadership challenge, but May appears to have emerged unscathed from a meeting of her party, for now", said Al Jazeera's Jonah Hill, reporting from London.
This tweet summed the whole thing up pretty well.
Mr Barnier refused to comment on the spate of resignations which wreaked havoc to on Monday, throwing the Prime Minister's Cabinet into turmoil.
Chequers mate: Theresa May ambush routs cabinet Brexiteers
On the worldwide markets, sterling slipped by a third of a cent against the dollar to $1.3288 in early trading. May has been reluctant to spell out her Brexit vision for fear of angering one faction or another.
Earlier, May defended her Brexit plan to lawmakers in the House of Commons, with Johnson absent from his usual place on the Conservative front bench.
Specifically, she wanted to address the resignations of Johnson and Davis.
It didn't take long for someone to get a Harry Potter reference in there, either.
May´s Conservative opponents could trigger a confidence vote against her if at least 48 MPs support it, but to actually force her from office 159 MPs would have to vote against her - a figure hardliners may not be able to reach.
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.
Roger Federer's brilliant response to question about Wimbledon and WC Final clash
Williams is looking for her eighth Wimbledon title and has established herself as the big favorite once again. The 36-year-old is also on a streak of 32 consecutive sets won at the tournament, just two off his record.
"It is as though we are sending our vanguard into battle with the white flags fluttering above them", Johnson wrote in a letter that underscored his credentials as a champion of full-speed Brexit.
Mr Barnier, the European Commission's chief Brexit negotiator, said it is become clearer for United Kingdom citizens what they will miss out after their country leaves the EU. The group of Tories Rees-Mogg speaks for won't support the Brexit plan as it stands, but Labour lawmakers said it wasn't yet close enough to their position to win their support. In one instance, he blamed Sinn Féin for Ireland's stance on the border.
With Britain due to leave the 28-nation bloc on March 29, 2019, European Union officials have warned Britain repeatedly that time is running out to seal a deal spelling out the terms of the divorce and a post-split relationship.
And in a rather dramatic fashion, news broke mid-way through the interview. Euroskeptic Conservative lawmaker Peter Bone said party activists felt "betrayed" by the government plan. "But I'm getting on with delivering what the British people want".
US judge extends deadline for reuniting migrant children
Officials said they were still working to locate the parents of numerous children, some of whom have been deported. For the other parents, I think there just hasn't been enough of an effort made to locate the parent.