Backbenchers have mounted a bid to topple the PM by putting in letters calling for a vote of confidence in her leadership.
But the Tory shop steward today shot down rumours that the revolt has attracted enough support to unseat Mrs May – meaning she is still safe for now.
Graham Brady, chair of the 1922 Committee of backbenchers, must call a vote of confidence if he gets 48 letters demanding one.
After Westminster insiders claimed the threshold had already been reached, Sir Graham told friends the rumours were wrong.
He is the only person who knows how many letters have been submitted at any given time.
During this morning's Cabinet meeting, Mrs May told ministers she is planning to produce weekly reports on the Brexit talks from now on.
The PM will also brief them regularly on how the Government is preparing for a possible No Deal scenario.
The briefings are meant to be a show of strength – proving to Brussels that the UK is ready for all possible outcomes.
Mrs May's spokesman said: "As we move towards exit day it makes good sense that all ministers are informed about the work taking place for both scenarios."
The PM told the Cabinet her priority is preparing for a withdrawal agreement, but stressed Britain will be prepared even if we leave the EU without a deal.
She said Brussels bosses will call an emergency Brexit summit as soon as enough progress has been made to secure a deal.
Amber Rudd today dismissed the idea that Mrs May could be unseated by furious Brexiteers.
She told the BBC: "I do think that she's safe – controversial I know.
"The fact is, whoever was leading the Conservative party now would have the same problem with the numbers. The numbers are that the MPs are divided on how to leave the European Union."
Mrs May received a boost from Brussels today as it was reported the EU is prepared to agree with her demands on the Irish backstop.
The PM wants to avoid striking a Brexit deal which would carve off Northern Ireland from the rest of the UK.
Her backstop proposal would see the whole of the UK stay in the EU's customs union if that was the only way to avoid a hard border in Ireland.
Brussels chiefs have previously resisted that suggestion – claiming it would be too difficult to sort out the details in time for Brexit.
But today RTE reported that the EU has accepted Mrs May's plans could be workable as long as both sides sign a separate treaty to enshrine it into law.
The compromise brings Britain and the EU a step closer to signing a deal which would ensure a smooth Brexit next year.
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