What happens next? Following are some scenarios. The government is trying to convince lawmakers to back the agreed stance, inviting them, including those from the opposition Labour Party, for briefings on the plan.
What appears to have kickstarted the resignations, however, is May's reintroduction of "collective responsibility", a British convention which means ministers are formally banned from disagreeing with government policy, including the Brexit plan.
He told the BBC a contest would take three months and "we physically do not have the time for that" given the United Kingdom is due to leave the European Union next March and both sides want a Brexit deal by October. "I won't be encouraging people to do that, I think it's the wrong thing to do".
But her spokesman signaled on Monday she would not back down over the "business friendly" agreement, saying May would now focus on moving the Brexit negotiations forward - a step European Union officials and businesses have long called for.
Before his letter of resignation was made public, Davis's allies told the British press that he was resigning because he could not support the soft Brexit plan pushed forward by May at a crunch cabinet meeting Friday at the prime minister's countryside estate, called Chequers.
"May's Brexit means BRINO - "Brexit In Name Only" - a fake Brexit", said John Longworth, co-chairman of Leave Means Leave.
Any attempt to replace May now would also put huge pressure on the government to call a general election, which would not only risk putting Jeremy Corbyn in power, but also threaten the whole future of the Brexit project. Major global businesses such Siemens, Airbus and BMW have called for a close post-Brexit relationship.
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Sterling rose, as traders bet Davis's resignation would not imperil May and instead focused on the newly-announced deal that markets believe makes a "soft Brexit" more likely.
The pound gained as much as half a percent to $1.3363, its best level since June 14.
But by appointing Brexit campaigner Dominic Raab as Davis's replacement, May might hope to quell some of that anger. May doesn't have a majority in Parliament so every vote counts.
The staunchly pro-Brexit Conservative lawmaker Andrea Jenkyns tweeted: "Fantastic news".
A leadership challenge can be triggered if 15 percent of members of parliament in May's Conservative Party write a letter to the chairman of the party's so-called "1922 committee".
While there may be at least 48 Conservative MPs willing to trigger a challenge against May, it is highly unlikely that such a challenge would ultimately be successful.
The PM's Brexit strategy was met with condemnation by many Eurosceptic MPs within her Conservative party, with many claiming the blueprint would be worse than "no deal".