"I don't detect any great appetite amongst my colleagues for presenting the public with a massive additional dose of uncertainty by getting involved in a self-indulgent Conservative Party internal election campaign.", Graham Brady, chairman of the 1922 Committee of Conservative lawmakers, told BBC TV.
The visibly weakened premier denied she was feeling "shell-shocked" when quizzed in an interview with Sky News.
Having failed to win an overall majority in the UK's general election, Theresa May's Conservative party is hoping to foster an informal coalition with Northern Ireland's Democratic Unionist Party (DUP).
She said May she will form a government that will provide certainty and work to keep Britain safe and secure.
European Council President Donald Tusk on Friday urged that Brussels and London should press ahead with the Brexit talks, in a congratulatory letter on May's re-election. The DUP is a socially conservative pro-British Protestant group that opposes abortion and same-sex marriage and once appointed an environment minister who believes human-driven climate change is a myth.
Ms Davidson's party won 13 seats in Scotland as its vote surged across the country.
Timothy and Hill, considered part of May's inner circle of confidants as her joint chiefs of staff, quit their Downing Street top jobs after coming under fire as the duo responsible for convincing May to call a snap general election with claims that she was assured a landslide victory.
Labour leader Jeremy Corbyn, riding a wave of acclaim for his party's unexpectedly strong showing, called on May to resign.
No 10 had earlier said the DUP had agreed the principles of a deal and it would be discussed at a cabinet meeting on Monday. From Labour? And is she likely to?
Instead, the election stripped May of her majority and obliterated her political authority. She is now going about forming a Cabinet.
As you can see, these are not well advanced plans but those who want something closer to a Norway type relationship with Europe sniff an opportunity and some of them think Theresa May staying in the job might suit their case, pressurising a wounded Prime Minister rather than risking a leadership election at the mercy of the Tory party members.
They are expected to make demands on Brexit negotiations and any deal with the DUP.
Political deadlock in London could derail Brexit negotiations with the other 27 European Union countries before they even get started in earnest - due to begin on 19 June. "In our view, the lack of a majority for any party is likely to delay Brexit negotiations, scheduled to start very soon", S&P Global said in an emailed statement.
Talks between the government and the DUP are due to restart Tuesday after confusion over the weekend whether an outline deal had been reached, but the Northern Irish party is in the driving seat as they know they are May's only option of forming a government.
London's neutrality is key to the delicate balance of power in Northern Ireland, which was once plagued by violence over Britain's control of the province.