The prime minister on Sunday promised to hold the meaningful vote in parliament in the week beginning 14 January despite growing opposition from Conservative backbenchers and the Democratic Unionist party, whose votes are required to push the deal through parliament.

As MPs prepare to return to Westminster with the crucial Commons vote looming on the withdrawal agreement, Downing Street insisted that new compromises could still be won from Europe that would ensure the safe passage of May’s plan.

The hope of new developments came as opposition to the prime minister’s deal hardened. The hurdles facing May include:

Brexiters say the government faces a disaster if it fails to ditch the current deal, with DUP deputy leader Nigel Dodds describing the Irish backstop as “toxic”.

• EU sources say talks to be held in Dublin on Tuesday between Leo Varadkar and Germany’s foreign minister, Heiko Maas, will not seek to reopen negotiations over the 585-page withdrawal agreement.

• Senior MPs including Yvette Cooper and Nicky Morgan are launching a parliamentary campaign to rewrite government legislation to block a no-deal Brexit.

• Chris Patten, the former Conservative Party chairman, called for a second referendum on the UK’s decision to leave the EU.

• More than 200 MPs have signed a letter calling for Theresa May to rule out a no-deal Brexit. Tory ex-minister Dame Caroline Spelman, who organised the letter with Labour’s Jack Dromey, said the group had been invited to see the prime minister on Tuesday.

In an interview on Sunday, May said the vote, which was due to be held last month and postponed, would go ahead next week, as she sought further clarification from the EU to address MPs’ concerns.

She also said she would look at giving parliament a greater say in how the UK’s future relationship would be negotiated, but refused to say exactly what that might be.

Asked if there had been any changes she could offer to backbenchers who were expected to vote down her deal, she told BBC1’s Andrew Marr Show: “What we will be setting out over the next few days are assurances in three areas: first are measures specific to Northern Ireland; the second is a greater role for parliament as we take these negotiations forward into the next stage for our future relationship; and third – and we are still working on this – is further assurances from the European Union to address the issues that have been raised.”

Whitehall sources insisted that a compromise could still be found with the EU and that further planned announcements will be made this week that would win over MPs opposed to the deal. “We will be working flat out. There will be further contacts with the EU leaders. The issue of the backstop is not yet over,” the source said.

In the interview, May repeatedly sidestepped questions about whether she would keep putting the deal back to MPs if it got rejected, instead saying: “If the deal is not voted on, this vote that is coming up, then actually we are going to be in uncharted territory. I don’t think anybody can say exactly what will happen in terms of the reaction we will see in parliament.”

Mark Francois, the vice-chair of the hardline-Brexit European Research Group, said May’s intervention on Marr showed that the government and the EU have little to offer their critics.

“As the prime minister herself once said, nothing has changed. No Conservative backbencher that I am aware of who was declared as against the deal has publicly recanted.

“The PM made very clear on Marr that the vote will go ahead at this time and that is good, because if they were to pull it a second time, as well as not being in power they would effectively no longer be in office.”

Conservative sources claim there are between 55 and 71 MPs who plan to vote against the deal.

The DUP, whose 10 MPs are required by May to force through the deal, remain opposed. Dodds said the government must stand firm and set out a “resolute red line” to Brussels. “The coming days will show if this government is made of the right stuff,” he said.

The government is also facing a serious challenge from a cross-party group of MPs seeking to block it from implementing no-deal measures without the explicit consent of parliament.

Amendments tabled by Labour former cabinet minister Cooper and Tory education secretary Morgan would restrict the government’s freedom to make Brexit-related tax changes without parliamentary safeguards.

The measure also has the support of Tories Sir Oliver Letwin, Nick Boles and Sarah Wollaston.

The UK is due to leave the EU on 29 March. May agreed her deal on the terms of the UK’s divorce and the framework of future relations with the EU but it needs to pass a vote by MPs. The Commons vote had been scheduled to take place in December but May called it off after it became clear that not enough MPs would back her deal.

Maas will fly to Dublin on Tuesday for Brexit talks with Varadkar, as they seek to find a fix to help get a withdrawal agreement ratified.

An informed EU source said Brexiters should not get their hopes up of a reopening of negotiations. The “fix” would be further details in the political declaration on the future relationship, and not the 585-page withdrawal agreement. “That is locked,” said the source.

A Downing Street spokeswoman said: “What we are doing is focusing on getting this vote through the House of Commons and getting those extra assurances required for MPs to support this deal that delivers on the referendum result – taking back control of our money, laws and borders while protecting jobs in the UK.”

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