Conservatives have given Prime Minister Theresa May 10 days to turn around her premiership before they demand a vote of no confidence, forcing her out of the job.
Confidence in May is at an all-time low after she failed to secure a majority in the general election and following the backlash she received for her response to the Grenfell Tower disaster, with currently at least 58 people missing and presumed dead.
Dozens of Tory MPs have since stated they are prepared to write to the backbench 1922 committee calling for May to quit if the tide is not turned soon.
A minister close to May told the Sunday Times: "She had better stop feeling sorry for herself, pull up her socks and start to lead – and if she can't do that she should go. Shape up or ship out."
Heidi Allen, the MP for South Cambridgeshire, gave a similar message stating that the public wanted "a leader and a party that will carry us through this most turbulent of periods but care about the little man... We have to change, and if we don't we deserve to die."
A number of Conservatives said 28 June was the cut-off date for momentum to be regained, when MPs will vote on the Queen's speech. If the Conservative-Democratic Unionist Party (DUP) alliance looks like it will not gain the support needed for the speech to pass, a leadership challenge will be mounted.
"If it looks like they [the vote on the Queen's speech] will be lost, you have to strike," a former minister told the Sunday Times.
The pressure on May comes as Eurosceptic Conservatives also threatened to oust her as prime minister if she attempted to water down Brexit, with some seeing the general election result as a backlash to "hard Brexit".
One Eurosceptic MP told the Sunday Telegraph that any attempt to keep Britain in the single market or the customs union would trigger an "overnight" coup.
Another former minister told the newspaper: "If she weakened on Brexit, the world would fall in... all hell would break loose."
Chancellor Philip Hammond was asked on the BBC's Andrew Marr Show on Sunday how long he thinks Theresa May has got.
He said: "What the country needs now is a period of calm while we get on with the job in hand. We have got some very serious issues to address, including the Brexit negotiations.
"Theresa is leading the government, and the government needs to get on with this job. And most people in this country will think the government just needs to get on with its day job of government."