British Prime Minister Theresa May will set out a blueprint on Thursday for what her government calls "a principled and practical Brexit", putting at its core a plan for a free trade area for goods that has angered many in her party.
Following Mr Johnson and Mr Davis's resignations, two deputy chairmen of the Conservatives - Ben Bradley and Maria Caulfield - quit their posts on Tuesday, claiming the PM's proposals would not harness the benefits of Brexit.
With less than nine months to go, it is a long-delayed decision and has not been without its consequences - Mr Davis and Foreign Secretary Boris Johnson resigned within hours of each other over a plan they said they could not defend.
Andrew Bridgen became the first Conservative MP to publicly confirm he had sent a letter calling for a vote of confidence in the prime minister, it was reported.
He has criticised May over her response to terrorism and approach to Brexit, and infuriated many in Britain when he retweeted a far-right group.
In comments likely to alarm Mrs May, Trump acknowledged the "turmoil" facing her government but said he was nevertheless looking forward to "an interesting time" when he visits the United Kingdom later this week.
But he warned he felt "very strongly about the future of my country" and said Tories had "real concerns" about the direction of Brexit.
The resignations have plunged her government into a crisis that could challenge her leadership and result in a no-confidence vote in parliament.
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Seven MPs including Boris Johnson and David Davis have quit their posts, condemning the Chequers plan for proposing too close a relationship with the European Union after Brexit.
Johnson, a polarising figure and a former mayor of London, was a leading spokesperson for the campaign calling for Britain's departure from the European Union in advance of a June 2016 referendum.
Much as arithmetic suggests that they now don't have the support inside the parliamentary party to dislodge the Prime Minister, time is a-ticking for the hardline Brexiteers. The Conservatives now have 316 MPs so 48 of them would need to write such letters to challenge May.
Mrs May received a rousing reception from the 1922 Committee of Tory backbench MPs on Monday night, although Mr Rees-Mogg said it was "delusional" to suggest that the meeting was indicative of the mood of the party.
In a policy paper, the government will outline proposals to allow Britain to maintain close economic and security ties with the European Union even after it leaves the bloc in March.
He said Brexiteers need to accept that pursuing a hard Brexit would likely fail to clear the Commons, risk thousands of job losses and threaten peace in Northern Ireland.
But many pro-Brexit lawmakers are furious at a plan they say will stop Britain forging an independent economic course.