Davis resigned yesterday, saying May's plan to maintain close trade and regulatory ties with the European Union gave "too much away, too easily".
If Davis's resignation rattled May, Johnson's shook the foundations of her government.
The campaign is fighting to give the public the final say on Brexit, a deal that is "too big to be ignored by the people".
Mr Kinnock said the Chequers proposal was a "step in the right direction because at least the prime minister was accepting that our future lies with Europe". "It is as though we are sending our vanguard into battle with the white flags fluttering above them".
"The trouble is that I have practised the words over the weekend and I find they stick in the throat". But furious lawmakers warned that she could split her Conservative Party trying to get her plan through Parliament.
Leaving the gathering, leading Brexiteer Jacob Rees-Mogg said he did not think there would be a confidence vote over Mrs May.
Mrs May said she was "sorry - and a little surprised" by Mr Johnson's move after his apparent support on Friday.
"That doesn't work, somebody else could do a better job than me".
Johnson quit on Monday over May's plan for Brexit, which includes a free-trade area for goods but little detail on the approach to services.
Under her proposal, a treaty would be signed committing the UK to "continued harmonisation" with EU rules - avoiding friction at the UK-EU border, including Northern Ireland.
‘It’s all propaganda, Russian people are the best!’
Many die-hard fans predict that Belgium is going to win while some others argue that France is going to notch the win. The video of her celebration in the VIP box in front of a visibly sad Russian PM has gone viral over social media.
Mr Barnier, the European Commission's chief Brexit negotiator, said it is become clearer for United Kingdom citizens what they will miss out after their country leaves the EU.
Government unity began to fray within hours.
And in a rather dramatic fashion, news broke mid-way through the interview.
He said many MPs saw Mr Johnson's resignation as a "selfish act".
On Monday, May defended Friday's deal, which would allow for some ties between Britain and the EU. The timetable increasingly looks overly optimistic, and European Union frustration with British division and chaos is growing.
"Now there is chaos", the paper said in its editorial.
May's personal authority was badly damaged after she called a snap election past year to strengthen her hand in Brexit talks but instead she lost her parliamentary majority meaning she has to rely on a small Northern Irish party to govern.
But May's allies fear more resignations may follow.
It started on Sunday night, when Brexit Secretary David Davis - ie. the man specifically appointed to ensure a smooth Brexit - chose to Brexit himself out of the actual government. She did not immediately name a replacement for Johnson.
Behind the scenes, European Union member states are fearful a collapse of Britain's minority Conservative Government would spell the end for Brexit negotiations and lead to a no deal. Euroskeptic Conservative lawmaker Peter Bone said party activists felt "betrayed" by the government plan.
"Nice try", she said with a touch of bravado.