The UK saw more political turmoil this week after two major cabinet resignations, and the housing industry is now faced with its 17th housing minister in 20 years.
The trans-Atlantic relationship has had some awkward moments since Trump's election.
Johnson has so far remained out of the spotlight since he resigned, and there has been little comment from potential leadership contender, leading pro-Brexit lawmaker, Jacob Rees-Mogg, who has been critical of May's proposals.
Labour MP Owen Smith, a supporter of the Best for Britain campaign for a second European Union referendum, said: "David Davis and the other resigning Tories are just the first of the rats to quit the sinking Brexit ship".
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.
"Boris Johnson is a friend of mine, he's been very, very nice to me", Trump told reporters before heading to Brussels for a summit of North Atlantic Treaty Organisation allies.
Stewart Jackson, former special adviser to Mr Davis, said No 10 had blocked his reappointment in the role under new Brexit Secretary Dominic Raab.
Conservative lawmaker Michael Fallon, an ally of May, dismissed Johnson's "Brexit dream" rallying cry.
When he entered Parliament in 2010, Raab said in an interview that David Trimble was the non-Conservative politician he most admired, "for taking the tough decisions that led to the Good Friday Agreement". Some 48 letters are required to trigger a vote.
"We need a vote for the people on the final Brexit deal and an opportunity for us all to flee this disaster". Mr Rees-Mogg refused to support her and said that "she would be well advised to revisit her Brexit policy".
International Trade Secretary Liam Fox said the Chequers agreement was created to be a "credible offer" to Brussels to allow negotiations to make progress.
"If anyone in the Conservative Party is then thinking about voting that down, that is the point at which they are going to endanger everything they have been trying to achieve". Pro-Europeans want to retain close economic ties with the bloc and its market of 500 million people, while some, but not all, Brexit supporters want a clean break to make it possible to strike new trade deals around the world.
Set to be published in a white paper on Thursday, the plan envisages Britain continuing to trade freely with the remaining European Union in goods under a "common rulebook", while accepting restrictions on trade in services. Analysts said the main reason why the Brexit debate has gone round in circles-and why the U.K.'s negotiations with the European Union have been nearly completely stalled for months-is that much of the British political class have never fully understood what the European Union is or how it works. Davis and Johnson initially backed the plan, before deciding they could not support it.
"We need to see the detail that sits in the white paper", said Phipson, "so this meeting was an important step for us". The British government is due to publish a detailed version of the plans on Thursday.