Theresa May is unlikely to have her Brexit deal passed on Tuesday, a senior member of her cabinet has admitted, as EU officials warned that a letter of assurances on the Irish backstop due to be unveiled on Monday contains nothing new.

In a statement to the Commons on Monday afternoon, the prime minister will try to win round MPs to her deal by publishing correspondence with the EU’s most senior officials.

The prime minister had promised she would secure additional “legal and political assurances” from Brussels when she delayed a vote on her deal and fought off a challenge to her leadership.

In a joint letter, Jean-Claude Juncker and Donald Tusk, presidents of the European commission and European council, are understood to emphasise that the backstop is a fallback option that they do not intend to trigger.

The customs union envisaged in the backstop, designed to avoid a hard border on the island of Ireland, would only be a temporary solution, and the EU would do its utmost to make swift progress on alternatives, they are expected to add.

The efforts that the commission will make to advance the trade talks will be spelled out in detail.

But EU officials have admitted that the letter will fall short of offering a date by when the backstop arrangements will be lifted, and fear that the prime minister has put too much faith in the last-minute gambit.

The British government will also publish a letter of intent when May stands up in the Commons. It is likely to lay out the dates by when the UK will seek to have a trade deal finalised, making the backstop irrelevant.

Juncker said on Friday, while in Bucharest for the opening of the Romanian presidency of the EU, that he would not offer anything that could be “confused with a renegotiation”.

In an admission of the weakness of the prime minister’s position before her Commons statement at 3.30pm, Liam Fox, the international trade secretary, conceded on Monday that while it was not impossible for the government to win the vote, it was nevertheless unlikely.

Fox also went on the attack to claim that parliament was “dominated by politicians that wish to remain in the European union” adding that “this is the basis of the problem we have”.

Fox called on MPs to show “humility” and “honour and respect” the referendum result. He added that blocking Brexit would “shake to its foundations the relationship between parliament and the voters of the country”.

A no-deal Brexit was “survivable”, he said, and those affected by it would adapt over time to the disruption. He echoed the recent claims of the transport secretary, Chris Grayling, by saying that a “no Brexit” would see a rise of “the populism we have seen in continental Europe”.

“I don’t regard no-deal as national suicide. This is not Dunkirk, this is leaving the European Union,” he told BBC Radio 4’s Today programme. “I think no-deal would damage our economy – I’ve been frank about that – but I think it’s survivable. I think no Brexit, politically, is a disaster from which we might not recover.”

May would outline to MPs “the assurances she had had from the European Union following discussions over the last few days”, Fox added.

Quick Guide Commons Brexit vote – the day's timetable Show 11.30am The Commons begins sitting. The first item is questions to Matt Hancock, the health secretary, and his ministerial team. These are meant to last 30 minutes but can run slightly over. Then the Labour MP Debbie Abrahams briefly introduces a private member’s bill on public sector supply chains under a 10-minute rule motion. After midday If there are no urgent questions or ministerial statements to delay proceedings, the final day of debate on Theresa May’s Brexit deal – officially known as section 13(1)(b) of the European Union (Withdrawal) Act 2018 – begins. It will be opened for the government by the attorney general, Geoffrey Cox. Before 7pm May will make a final closing speech for the government, appealing for support for her deal. From 7pm Voting begins. However, before the crucial vote, MPs must vote on the four amendments accepted by the Speaker. One amendment, tabled by the Tory Hugo Swire, has been accepted by the government. At some point between around 7.30pm to 9.30pm MPs finally vote on the deal, as amended.

If May is defeated she is likely to face a no-confidence vote tabled by Labour. The shadow chancellor, John McDonnell, declined to say precisely when this would happen, but indicated it would be soon. “The call will be made tomorrow after that vote,” he told Today.

With May and her ministers refusing to outline what alternative plan might be put forward if her proposal was defeated, a series of backbench ideas have been unveiled to seize control of the process from government.

Om Monday, a cross-party group of MPs from the Lib Dems, Labour, Conservatives and SNP were publishing two draft bills designed to pave the way for a new referendum. One of these would give voters the option of voting for the government’s deal or staying in the EU.

Separately, three senior Conservative backbenchers drafted a bill that would give the liaison committee, which groups together the MPs who chair various select committees, a key role in coming up with a new plan.

Nick Boles, who has come up with the idea along with Nicky Morgan and Oliver Letwin, said all three would vote for the PM’s deal on Tuesday, but would act if it failed.

Boles told Today their planned bill would give May a further three weeks to come up with a compromise deal and get it through parliament. If that failed the liaison committee would be given “the responsibility to try and come up with its own compromise deal”.

He added: “If the house passed that compromise deal, then the government would be legally required to implement whatever it was that they had.”

Boles is among Tory backbenchers accused by some newspapers of trying to stage a “coup”. Asked about this, Boles said: “It’s a funny kind of coup which requires a majority vote of democratically elected MPs before the task starts rolling. So, no, it isn’t a coup, it’s an expression of parliamentary will.”

Similar accusations have also been levelled against the Tory former attorney general Dominic Grieve, one of the MPs tabling the proposed bill on a new referendum. At the weekend, some newspapers said he was leading a coup against Brexit in alliance with the Commons Speaker, John Bercow.

Grieve, whose amendment obliging May to respond to the defeat of her plan within three days was passed by MPs last week, told the Guardian the reports were “rubbish”, and had resulted in him receiving death threats.

“I can emphatically say it is totally untrue that I am in a conspiracy with the Speaker either to stop Brexit or to change the standing orders of the house,” he said.

In her speech, at a factory in Stoke-on-Trent, where more than two-thirds of people voted to leave the EU, May will reiterate her claim that a rejection of her proposals on Tuesday would destroy faith in politics, and could mean that Brexit does not happen.

“I ask MPs to consider the consequences of their actions on the faith of the British people in our democracy,” she is due to say.

“What if we found ourselves in a situation where parliament tried to take the UK out of the EU in opposition to a remain vote? People’s faith in the democratic process and their politicians would suffer catastrophic harm. We all have a duty to implement the result of the referendum.”