As the Conservative Party digested the loss of its majority in last week's election, government officials suggested both the announcement of the prime minister's agenda, known as the Queen's Speech, and talks over Britain's divorce from the European Union could be postponed.
On Monday afternoon, Theresa May will meet with the 1922 Committee, a parliamentary group that comprises Conservative backbenchers - a term which applies to any lawmaker who sits behind Cabinet ministers on the government's front bench in the House of Commons, Efe news reported.
Anna Soubry, a Conservative member of Parliament, said she could not predict when May might go, but called the prime minister's position "untenable".
Mr Davis added: "In the first round we are going to have pretty long meetings at roughly one week a month - which is much, much faster than any previous trade deal they have done".
British Prime Minister Theresa May is in for a hard Tuesday as she is due to hold talks with Northern Ireland's Democratic Unionist Party to secure an informal alliance before meeting French President Emmanuel Macron in Paris.
The EU has said that Brexit talks need to make sufficient progress before trade deals can be discussed, though Britain had argued the discussions should take place simultaneously.
May went from vowing to bring about Brexit successfully and cutting back immigration, another popular demand, to essentially going after animals and the elderly.
Former Northern Ireland Secretary Lord Hain is concerned, along with the Taoiseach in waiting - Leo Varadkar, who says as co-guarantors of the GFA, neither Government can be too close to any party.
Environment Secretary Michael Gove says it is vital that the government can "achieve a deal that can command the widest possible support".
May to face party lawmakers after election disaster
To stay in power, the Conservatives are seeking support from Northern Ireland's Democratic Unionist Party. Writing in the mass-circulation Sun newspaper, Johnson stressed that the Conservatives won more votes than at any time since Margaret Thatcher and are still the largest party in Parliament.
During the campaign, Ms May cast herself as the only leader competent enough to navigate the tortuous Brexit negotiations that will shape the future of the United Kingdom and its $2.5 trillion economy. However, the bigger problems for the Tories may be that the party has been supportive of a "soft Brexit", not the hard option wanted by the Prime Minister.
British Prime Minister Theresa May gives a speech at 10 Downing Street after meeting with the Queen in London, Britain on June 9, 2017.
The first test of any deal is expected to come at the Queen's Speech - which has been delayed today.
Labour supporters on the other hand have not given up on the idea that Corbyn might well become Prime Minister yet, a fantasy that is not supported by numbers. But there has been concern in Dublin and among nationalists in Northern Ireland about concessions that might be secured by the DUP, which is also negotiating to restore the power-sharing institutions at Stormont.
"You're going to see in the next few weeks her taking back command, her taking back the reins, her showing what she's good at, which is delivering for the country", he said as he sought to soothe over the political turmoil that has gripped the government since Thursday's election.
The announcement surprised the DUP, which said that talks were still continuing as Gavin Williamson, the chief whip, held discussions in Belfast.More news: Three ways to celebrate Pride Month on Facebook