Dozens of normally loyal Conservative MPs could rebel against the government in a bid to prevent a no-deal Brexit, Downing Street has been warned.
Leaders of the Brexit Delivery group of MPs, comprising Leavers and Remainers, say up to 30 may back alternatives if the PM's reworked deal isn't voted on.
No 10 says talks aimed at getting the changes MPs demand continue "at pace".
Meanwhile, John McDonnell has suggested Labour is "moving towards" backing another Brexit referendum.
The shadow chancellor told the Evening Standard he was warming to the idea of MPs backing a Commons amendment which would approve the Brexit deal but only if it was put to the public in another vote.
Theresa May's efforts to win round European leaders will continue at a summit in Egypt over the weekend.
Her spokeswoman said the PM would have another "period of engagement" on Brexit at an EU-League of Arab States summit in Sharm el-Sheikh - including a meeting with European Council president Donald Tusk.
But a senior EU official said there would be "no deal in the desert", since not all the 27 other EU leaders would be present and the issue required proper preparation.
The UK remains on course to leave the European Union on 29 March.
But the government has repeatedly refused to rule out the possibility of the UK leaving without a formal deal, in the event that Mrs May cannot get MPs to approve the deal she negotiated with Brussels in time.
On Friday, the Irish government published a wide range of emergency measures to support businesses, protect jobs and essential services that will be enacted if the UK leaves the EU without a deal.
Many MPs fear that scenario would be damaging to business and cause chaos at ports.
Growing concerns over the prospect of a no-deal exit are set to come to a head next Wednesday when MPs debate Brexit again and, if the UK and EU haven't agreed a deal by then, will vote on future options.
The Brexit Delivery Group (BDG) says "numerous" Tory MPs are prepared to back an amendment tabled by former minister Sir Oliver Letwin and Labour's Yvette Cooper to give Parliament the opportunity to delay Brexit and prevent a no-deal situation if there is no agreement with the EU by the middle of March.
It has been reported that a handful of ministers, including potentially some in the cabinet, could also back the amendment, in what would be a direct challenge to the prime minister's authority.
The BBC's Newsnight's political editor Nicholas Watt said a number "were saying in private they would be prepared to lose their jobs" to be able to support the amendment.
BDG co-chairman Andrew Percy told the BBC that members of his group were becoming "tired" of the rival European Research Group faction's refusal to back the prime minister.
The ERG of Brexiteers, led by Jacob Rees-Mogg and Steve Baker, insist the "no-deal" option must be preserved as negotiating leverage in Brussels and declined to back the PM in a non-binding vote on the issue recently.
In a letter to government whips, Mr Percy and his co-chairman Simon Hart write: "Not only does this risk damaging the national interest, but also... we are putting in jeopardy the very thing many colleagues have spent decades campaigning for; our exit from the European Union."
They believe the main sticking point - MPs' demands for changes to the backstop, the "insurance policy" to prevent the return of customs checks on the Irish border - will be secured.
However, they fear it might not be enough to win over some Brexiteers.
One ERG member, Nadine Dorries, insisted the group was not "holding the government to ransom", telling the BBC's Politics Live that all but one member was "desperate for a deal".
Reaching out to Remainers
On Thursday, Mrs May held meetings with senior ministers who have expressed concerns about the impact of a no-deal scenario on business and also leading Remainers in her party, such as Justine Greening and Phillip Lee.
The duo have been touted as potential defectors to the newly formed Independent Group of ex-Tory and Labour MPs, which is calling for another EU referendum in return for supporting the PM.
Mr Lee told the BBC that although he was staying in his party, there were "worrying" signs of a "populist" shift in direction and it was time for Mrs May to "face down" the ERG.
"There are elements of that group that do not reflect the Conservatism that I joined in 1992 and it's about time that we dealt with it," he told Radio 4's Today.
The government has described the latest talks in Brussels involving Brexit Secretary Stephen Barclay, Attorney General Geoffrey Cox and EU chief negotiator Michel Barnier as "productive".
It says they will move to a "technical level", with Mr Barclay and Mr Cox meeting Mr Barnier again early next week.