In an interview yesterday, Mrs May responded to reshuffle questions by insisting she would not "hide from a challenge".
"Goddammit she's the prime minister of a G7 country, she didn't get there by luck or by default".
Writing in the The Sun on Sunday, David Cameron's former director of communications Craig Oliver said the prevailing wisdom in the party is that any leadership contest now, with Brexit unresolved and Labour buoyant, "would result in bloodshed and highlight division".
But senior Conservatives loyal to the Prime Minister are striving to move on from the party's post-conference turmoil, with Culture Secretary Karen Bradley claiming more than 90% of Tory MPs are in support of Mrs May.
The Observer newspaper said unnamed senior Conservative figures said while May had no long-term future they were pressing her to shake up her team of ministers, hoping new blood would re-energise the party as well as frustrate Johnson's ambitions. "I'm absolutely certain from what I know that Boris doesn't want this nonsense to be going on".
Mrs Sturgeon had planned to hold a second vote on leaving the United Kingdom between autumn 2018 and spring 2019, but was forced to put those plans on hold after the SNP lost 21 of its MPs in June's snap general election.
"That's not a very large number when you look at another almost 300 who are determined to keep her in place", she added.
But within hours, his allies began to rally round - saying that Boris could "just say no" to a new job, and warning that pro-Brexit voters need a champion at the top of the Government.
A nagging cough and a failing voice added to British Prime Minister Theresa May's political woes this week, but the weekend saw her staying on in 10, Downing Street, as a new challenge to her leadership collapsed and her ambitious foreign secretary Boris Johnson fell in line. If you were a Brexiteer you would be anxious [if Johnson was sacked].
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"But I think it is nearly unbelievable that the Prime Minister could have Boris Johnson in the position as Foreign Secretary".
Mrs Bradley, who served the PM during their time together in the Home Office, dismissed reshuffle talk as "speculation", but delivered a public rebuke to Mr Johnson over his controversial remarks at a Conservative conference fringe event.
The reshuffle, according to the Sunday Times, would take place after an October 19-20 summit in Brussels where May will be hoping for a breakthrough few think possible.
She told ITV's Peston on Sunday: 'If I were the Prime Minister, the person I would be demoting or certainly sacking would be Philip Hammond.
Ms. Davidson told BBC One's Andrew Marr Show the Foreign Secretary had backed Mrs.
"If that was just a problem for the Conservative Party I wouldn't be particularly bothered, but it's a massive problem for the country at the moment", the SNP politician added.
A minister told The Telegraph: 'Let's say she tries to move Boris to defence secretary.
"I do not know who these people are".