The Prime Minister has been urged to face her backbenchers after tensions flared over her Brexit plans following a Brussels summit.
David Davis, who is tipped as possible successor to Mrs May, said the PM had “managed to anger not just Leavers but ardent Remainers as well”.
The former Brexit secretary insisted “we should not allow ourselves to be bullied by the EU” and warned the bloc has plenty to lose from a no-deal Brexit.
Writing in the Mail on Sunday, he warned: “There have been claims that planes will not fly between the UK and EU. This is extremely improbable as it would undermine the Spanish and other European tourism markets as well as Mediterranean property markets.
“Furthermore, European flights would still need our airspace in order to fly to the USA. That should be enough to focus minds on a sensible outcome.”
Critics of the PM claim the 48 letters needed to trigger a no confidence vote could soon be reached.
Andrew Bridgen, a long-standing critic of Mrs May, told the newspaper she must attend a meeting of the Tory 1922 committee of backbenchers on Wednesday.
He said: “This week Theresa May will find that she is drinking in the last chance saloon and the bad news for her is that the bar is already dry.
“If she doesn’t turn up to the ‘22 that will only make the letters go in even faster.”
No 10 sources said Mrs May’s diary would be set out on Monday.
Brexit Secretary Dominic Raab indicated the UK must not extend the transition period unless Brussels drops its demand for a backstop on the Irish border.
In The Sunday Telegraph, he wrote: “The Prime Minister has rightly refused to rule out considering different approaches - including extending the implementation period, as an alternative to the backstop.
“But we won’t sacrifice Northern Ireland, and we must have finality to any backstop - whether through a time limit or a mechanism that enables the UK to leave, in case the EU doesn’t live up to its promise to get the future relationship in place swiftly.”
Meanwhile, former Brexit minister Steve Baker is attempting to block the backstop with changes to legislation being heard by Parliament.
His proposed amendments to the Northern Ireland (Executive Formation and Exercise of Functions) Bill would make it a legal requirement for the Stormont Assembly to agree to any plan to treat Northern Ireland differently to the rest of the UK.
The devolved legislature has not sat at Stormont since power-sharing broke down in January 2017.
The Bill is due to go before the House of Commons on Wednesday.
The logjam in the Brexit negotiations has left the PM fighting criticism on several fronts, including from an MP seen as a rising star in the Tory party.
Johnny Mercer, who earlier this week branded the Government a “shitshow”, said he had received “overwhelming” support from within the party after speaking out.
He told The Sunday Times: “I cannot continue to support an administration that cannot function.”
Labour, meanwhile, warned Mrs May that if she is hoping they will help pass her Brexit blueprint she can “think again”.
Sir Keir Starmer said the current deadlock is a “mess of the Prime Minister’s own making” and warned she is unlikely to survive if she cannot secure support for her plans.
The shadow Brexit secretary dismissed claims that 90% of the exit agreement is complete because the remaining chunk is the “difficult bit”.
In an article for the Sunday Times, he wrote: “To say that things have gone very wrong is an understatement.”
He added: “Things could - and should - have been different. But at no stage has the Prime Minister ever reached out to Parliament or sought to build a national consensus on our future relationship with the EU.
“The current deadlock is a mess of the Prime Minister’s own making. And if she thinks Labour should prop her up because her own team won’t back her, she can think again.”
Sir Keir said Labour has been clear that it would support a Brexit deal that builds an economically close relationship with the EU, but claimed the PM had “never taken up the challenge of negotiating that deal in the national interest”.
“She is fast running out of road,” he added. “There can be no more failed summits. If she can’t command the support of her cabinet, her party or parliament, more fundamental change will inevitably follow.”