The prime minister is facing calls to resign amid a backlash against her Brexit plan from Conservative MPs.
There have been growing calls for her to quit from her own MPs unhappy with the compromises she has set out in her Withdrawal Agreement Bill.
Several cabinet ministers have told the BBC that Mrs May cannot stay on, while others insisted she must present her plan to the Commons.
The PM told the Commons there needed to be “compromise on all sides”.
The BBC’s political editor Laura Kuenssberg also said the so-called “Pizza Club” of Brexiteer cabinet members have been meeting while Mrs May was answering questions in the House – a move she described as “a bad omen for the PM”.
She added that Home Secretary Sajid Javid says he had asked to see the PM to push her to remove the second referendum vote requirement contained in the Withdrawal Agreement Bill.
Mrs May told MPs that the bill – which includes the promise of a vote on a further referendum and different customs options – would be published on Friday.
The PM has pledged to set a timetable for a new leader to take over after MPs vote on her compromise Brexit plan in the week beginning 3 June.
However, some MPs are again seeking to change party rules, so they can vote to oust her at a meeting of backbench MPs.
Labour has also criticised Mrs May’s new plan, with its leader Jeremy Corbyn saying her “bold new deal” was a “repackaged version” of her withdrawal agreement that has been voted down in the Commons three times.
He added: “No Labour MP can vote for a deal with the promise of a prime minister who only has days left in her job.”
Mr Corbyn said the issue of Brexit had been “dividing our society and poisoning our democracy”, but claimed Mrs May’s deal “does not represent a genuine compromise”.
Addressing her critics in her speech, Mrs May said: “In time, another prime minister will be standing at this dispatch box, but while I am here, I have a duty to be clear with the House about the facts.
“If we are going to deliver Brexit in this Parliament, we have to pass a Withdrawal Agreement Bill, and we will not do so without holding votes on the issues that have divided us the most,” she said.
“In the end, our job in the House is to take decisions, not duck them.”
Stand firm and push on
Conservatives I spoke to commented on Theresa May’s position with a mixture of sympathy and derision.
One long-standing Brexiteer described PMQs as her leaving party. Another Leaver simply muttered tersely that it was “grim”, while a Remainer, who had been prepared to back her deal, mulled “why is she putting herself through any more of this?”
Inside Downing Street, there is a recognition that there will be an attempt to oust Mrs May before her Brexit deal gets as far as a vote.
The intention is to stand firm and push on.
But there is an understanding of how difficult it will be.
Read more from Iain Watson here
The 1922 Committee – made up of Conservative backbench MPs – is due to meet at 17:00 BST, after a meeting of the executive.
The current rules dictate that the group can hold a vote of confidence in their party leader if the chairman of the committee, Sir Graham Brady, receives letters calling for it from 15% of the parliamentary party – currently 47 MPs.
However, as the PM survived such a vote in December, the rules say she cannot face another one for 12 months.
One of the 1922’s executive secretaries, Nigel Evans, wants this overturned and has said he will propose a change to the group’s rules to allow for a no confidence vote to take place against Mrs May immediately.
An earlier attempt to do this failed – but Tory MP Tim Loughton tweeted a picture of a letter to Sir Graham, adding: “Enough said.”
On Tuesday, the prime minister asked MPs to take “one last chance” to deliver a negotiated exit – or risk Brexit not happening at all.
But it immediately led to criticism from both Leave and Remain-backing MPs.
Brexiteer Sir John Redwood said there were “millions of angry leave voters who do not see the agreement as any kind of Brexit, but a lock in for many, many months with no clear way out”.
His fellow Leave voter and Tory MP, Priti Patel, called the bill “a slippery slope to keep us in the EU”.
The SNP’s leader in Westminster Ian Blackford – who supports a further referendum to remain in the EU – said it was time for the prime minister to go, having “lost the trust of the public”.
“This deal is dead,” he added. “Stop this charade and let’s get on with putting this decision back to the people once and for all.”
Labour’s Liz Kendall backed the call for a public vote, telling Mrs May she will not get enough support for her bill from opposition members without including a confirmatory ballot as part of the deal – rather than just offering a vote on whether to have one.
But Conservative MP Vicky Ford said: “We cannot continue to leave our country in this uncertainty. It has to stop. The whole House has to stop saying no to everything on the table just because it is not our favourite dish.
“If we vote for this bill we can move on and the discussion on the next stage can start.”
What is in the Withdrawal Agreement Bill?
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Mrs May is bringing the Withdrawal Agreement Bill – legislation required to bring her agreement into UK law – to Parliament in early June.
In an attempt to win over MPs across the House, she announced the following concessions:
- A guarantee of a Commons vote on whether to hold another referendum on the government’s Brexit deal
- A vote on different customs options, including a government proposal for a temporary customs union for goods – what Mrs May called a “customs compromise”
- A legal obligation for the UK to “seek to conclude alternative arrangements” to replace the Northern Ireland backstop by the end of 2020
- If the backstop does come into force, the bill would guarantee Northern Ireland remains aligned with the rest of the UK and remains in same customs territory
- Legislation to ensure workers rights are “every bit as good, if not better” after Brexit – and guarantees of no dilution in environmental standards
- A legal duty to seek changes to the political declaration on future relations with the EU