But May said talks with European Commission chief Jean-Claude Juncker, EU President Donald Tusk and other EU leaders at the weekend suggested her plan "can ensure that we move the negotiations on".
"Good riddance, Boris Johnson" reads the headline on an online opinion piece by the New York Times' editorial board.
"I get along with her very well, I have a very good relationship", he said.
Picture: AAPJeremy Hunt was appointed foreign secretary following Johnson's resignation.
Mr Hunt was a Remain campaigner in the referendum - although he has since declared he is a convert to the cause of Brexit - and his appointment will be seen as a tilt in the balance at the top of the Cabinet.
One East Anglian MP, speaking off the record, said: "I am not entirely surprised as he is a bit of a maverick, and if cabinet-level resignations are limited to DD then I think the prime minister will probably survive".
The Government went on to explain that it held Brexit discussions with senior officials from the UK Government yesterday afternoon, as the two Governments continue to work closely together going forward.
Trump also added to the sense of chaos surrounding the Government when he described the United Kingdom as being in "turmoil" and said it was "up to the people" whether or not May remains in power. Jeremy Wright, Geoffrey Cox, Chris Heaton-Harris, Kit Malthouse and Justin Tomlinson all receive promotions and their names were swiftly googled by many in Westminster.
"Dreaming is good, probably for all of us, but we have to deal with the real world", he said.
Describing the Queen being greeted in Commonwealth countries by "flag-waving piccaninnies", a derogatory term for black children, and then-prime minister Tony Blair being met by "tribal warriors" with "watermelon smiles" while on a trip to the Congo.
Pro-Europeans want to retain close economic ties with the bloc and its market of 500 million people, while some Brexit supporters want a clean break to make it possible to strike new trade deals around the world.
The negotiations with the European Union appear to have deteriorated into a state of complete capitulation.
In 1982, three foreign office ministers quit, taking responsibility for Argentina's invasion of the Falkland Islands. The Prime Minister is the person who makes the final call in relation to Britain's position on Brexit. (Indeed, any Conservative prime minister who lost their majority in an election called because of massively favourable opinion polls wouldn't usually last a few days, never mind more than a year.) But these times are far from "normal" - and as it stands, it's hard to see who in their right mind would want to take over from May right now considering the mess they would inherit.
"The Government now has a song to sing".
Ian Lavery, chairman of the main opposition Labour Party, said, "This is absolute chaos and Theresa May has no authority left".
He told the programme: "What we are trying to do is not open revolt but we are trying to tell the Prime Minister and the Cabinet that we have got real concerns about where this is going".
May has said she will fight off any attempt to unseat her.
Addressing Parliament on Monday, May told MPs that she and the two ministers were at odds over "the best way of delivering our shared commitment to honoring the result of the referendum".
Mr Johnson appeared to laugh when the caller said he was a holding a meeting with the Russian president and that he "hoped he will not poison me with novichok".