An early recess might not stop a potentially stinging resignation statement from Boris Johnson.
Mr Davis' resignation was the first in a long line of Government departures over the Chequers soft Brexit plans, and they came to include former Foreign Secretary Boris Johnson. Britons should be "great independent actors" on the world stage, not "rule takers", he said.
"The only solution is to take the final Brexit decision out of the hands of deadlocked politicians, away from the backroom deals, and give it back to the people", she said in an article for The Times.
An accidental Prime Minister, stuck with a job that she did not choose for herself, May is faced with the dual task of negotiating with the European Union while at the same time not deviating much from the ultimate objective of Brexit for which almost 52% of the British population had given their nod. "If we don't, we risk ending up with no Brexit at all", said May.
May claims that the trade bill will enable Britain to maintain the 40-odd trade agreements that the European Union has with countries around the world.
Johnson backed a "global Britain", saying he wanted British people to be "champions and catalysts for open markets, and militate ceaselessly for free trade deals".
While Mr Johnson was cautious not to attack the Prime Minister personally, he pulled no punches over her Chequers deal, which he said amounted to "Brexit in name only" and he was unable to accept it or support it. With May's support faltering, members of her own party, including Davis, felt emboldened to ask critical questions about her way forward.
Parliament will debate aspects of the Brexit proposal later Monday, when May will face efforts by hard-line Brexit backers to use a series of amendments to limit her government's ability to set up the customs arrangement she seeks - one that would keep close ties with the EU.
However, the danger to the Prime Minister was underlined by the disclosure that Brexiteers had set up a WhatsApp group to co-ordinate voting tactics, organised by ex-Brexit minister Steve Baker, who quit over the Chequers plan.
Shouts rang out across the Commons.
A bristling Mrs May insisted at "absolutely no point" had that happened because "Brexit continues to mean Brexit".
Johnson told lawmakers that the government had "dithered" and failed to make the case for a free trade agreement outlined in the January 2017 speech at Lancaster House in the heady months after the referendum passed.
In a series of votes, May could come under attack from arch-Brexiteers in her own Conservative Party who think her plans have watered down Brexit and will leave Britain shackled to the European Union once it leaves the bloc in March.
"Not the democratic disaster of ongoing harmonisation with no way out and no say for the UK".
Time is of the essence as resigning foreign secretary Boris Johnson, believes the United Kingdom can still negotiate a "great" Brexit deal.
Mrs May will try to rally her deeply divided parliamentary party as she addresses a meeting of the 1922 Committee of backbenchers in the evening.
She received at least a measure of support from the 1922 Committee, including the announcement by one lawmaker that he had withdrawn a letter calling for a confidence vote that could threaten May's position as party leader.
Business Secretary Mr Clark was challenged about the potential revolt on the Taxation (Cross-border Trade) Bill, often referred to as the customs bill.
Gregory Katz in London contributed.