The Conservative leader will hold a crunch meeting with restive backbenchers this week amid anger over the government’s handling of negotiations with the EU.
One unnamed Tory MP suggested she should “bring her own noose” while others said Mrs May is entering a “killing zone” and that “assassination is in the air”.
Brexit Secretary Dominic Raab called for unity among his fellow MPs yesterday, urging them to “play for the team” and “hold their nerve”.
He also suggested the Brexit implementation period – due to end in December 2020 – could be extended by three months.
But with Mrs May’s minority administration already facing a struggle to secure the votes of enough MPs to get any deal endorsed in the Commons, Scottish Conservative MPs are now warning they will not back any extension to the implementation period. They say such a delay would bind Scotland’s fishermen to the common fisheries policy.
Douglas Ross, Conservative MP for Moray, said a three-month extension would be unacceptable to him and indicated he and his Scottish colleagues would abstain in a vote on the deal.
He said: “I was disappointed when the implementation period was extended until December 2020 and I think it’s important that we give a very clear message.
“I’ve given that in Moray to my constituents in coastal communities such as Buckie that I cannot support a deal that keeps us in the common fisheries policy any longer than December 2020.” Asked whether there is unanimity among Scottish Tory MPs on the issue, Mr Ross added: “That is my understanding.”
He added: “I do think there is unanimity across Scotland that people see fishing as a particularly important negotiation for the Brexit negotiations and that means we must come out of the common fisheries policy.”
Scottish Secretary David Mundell said last week he would not support any extension to the implementation period.
Mr Raab insisted there must also be a route out of any extension so that it did not run indefinitely. “It could be time-limited, there could be another mechanism,” he told BBC One’s The Andrew Marr show.
A meeting of European Union leaders in December has been spoken of as the final deadline for striking a deal.
But Mr Raab said he believed the exit agreement needed to be done “towards the end of November” to allow time for legislation to be passed.
Mrs May is to appear before a potentially explosive meeting of the Tories’ 1922 backbench committee on Wednesday which has already been branded a “show trial” by one MP.
There is also speculation that former Brexit secretary David Davis has stepped up efforts to replace her as leader. Internal opponents are said to have 46 backers for a contest – two short of the total needed for a leadership challenge.
Asked about the growing criticism of the Prime Minister, Mr Raab said: “We are at the end stage of the negotiations. It is understandable that there are jitters on all sides of this debate.
“We need to hold our nerve. The end is in sight in terms of a good deal, the prize we want.
“I think colleagues should wait and see what that looks like. It won’t be a question of a fait accompli. They will have their full say over it.”
He added: “Now is the time to play for the team.”
Brexit minister Suella Braverman said any extension to the transition period must not leave the UK “exposed to indefinite membership of the customs union”.
Mrs Braverman, a leading Brexiteer, said there are “many views” about the Prime Minister’s Chequers plan for trade relations.
She told Sky’s Sophy Ridge On Sunday: “I see Chequers as a pragmatic proposal.”
Mrs Braverman did not condemn anonymous Tory MPs who told newspapers that Mrs May is in a “killing zone” and should “bring her own noose” to the meeting with backbenchers.
She said: “Colleagues are free to express themselves in the way they wish but I am very clear that our party is stronger when it’s united.”
But former Tory minister Robert Halfon said: “I say to the people giving those quotes, this is not the way to change things.”
Mr Halfon said the Conservatives had a “serious image problem” and warned that voters think the party is just about austerity or Brexit.
But he dismissed suggestions it was time to replace the Prime Minister. “I don’t think a change of leader would particularly help, particularly in the middle of Brexit,” he said.
First Minister Nicola Sturgeon also condemned the language used in the attacks on Mrs May, writing on Twitter: “Few disagree with her more than I do, but language like this debases politics.”
Labour, meanwhile, warned Mrs May that if she is hoping its MPs will help pass her Brexit blueprint she can “think again”.
Labour’s shadow Brexit secretary Sir Keir Starmer said there is a “lack of confidence” that she can bring back “anything by way of a good deal” and that it was not in the national interest to back a bad deal.
At least 670,000 people turned out for Saturday’s People’s Vote march, organisers claimed, making it the biggest anti-Brexit demonstration since the referendum in 2016.