Their resignations came after May chaired the first meeting of her new cabinet following the departure of Johnson and David Davis.
Boris Johnson has been a friend of the president, was a friend during the election and he has a warm and close relationship with the president.
Ben Bradly's letter of resignation struck a similar tone, saying: "I have come to the conclusion that I can not in good faith be a spokesman for the party or for Government on this issue" of the government's Brexit position.
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.
The Daily Telegraph said on Tuesday night that senior Brexiteers said that they have enough letters in hand to trigger a confidence vote and will submit them unless she hardens her Brexit plans.
Amendments lodged by the head of the European Research Group of pro-Brexit backbenchers and supported by MPs including the Scottish Conservative Ross Thomson would block the government from keeping one foot in the EU customs union for goods, and prevent a proposed "backstop" solution for the Irish border from creating an internal trade boundary in the Irish Sea.
In the pro-Conservative Spectator magazine, Brendan O'Neill wrote that there had been "a Remainer coup" - a reference to Johnson's replacement Jeremy Hunt, who also supported staying in the European Union but says he has now changed his mind.
In the immediate aftermath of the Cabinet signing up to Theresa May'ssoft Brexit strategy on Friday, the odds of a Conservative leadership contest in 2018 were 2/1.
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.
Speaking at the Institute of worldwide and European Affairs in Dublin, Minister Coveney said there had not been a clear British negotiating position for many months.
Unhappily for May, his most effusive praise was reserved for the outgoing foreign secretary. We need to rise to the challenge and grasp the opportunities'.
On Thursday, the government proposal or White Paper was due to be published, setting out the terms for Britain's exit from the European Union and its future relations with the bloc after March 2019.
"We deliver that Brexit and we do it in a way that protects jobs and livelihoods and meets our commitment to Northern Ireland", she said.
Four out of five readers who took part in our survey said the Brexiteer big beasts were right to quit the Cabinet, a move which has been widely praised by many of those to the right of the Tory party.