MPs have begun putting forward proposals to change the outcome of Brexit ahead of next week's scheduled vote on Theresa May's amended deal.
May will meet her cabinet after telling MPs on Monday that she was focused on altering the Irish backstop.
But Labour leader Jeremy Corbyn said the prime minister was in denial about the level of opposition to her deal.
Among the MPs' amendments are plans to prevent a no-deal Brexit and to extend the deadline for leaving the EU.
MPs are due to vote on a modified version of May's deal on 29 January.
On Monday, the PM vowed to seek changes to the Irish backstop from the EU and also scrapped the £65 fee EU citizens were due to pay to secure the right to continue living in the UK after Brexit.
However, she gave few details about how her deal would be changed before next Tuesday's vote.
Speaking to BBC Radio 4's Today programme, Conservative MP Iain Duncan Smith, who voted against May's deal, said the backstop was "unworkable", adding that he also had objections to the £37 billion so-called divorce bill the UK was preparing to pay the EU.
'Brexit deadlock'
Corbyn said the amendment allowed MPs "to end this Brexit deadlock" and prevent the "chaos" of leaving the EU without a deal.
But May warned that another EU referendum could threaten the UK's "social cohesion".
Among the other plans being put forward by MPs are:
An amendment by Labour MP Rachel Reeves aimed at preventing a no-deal Brexit by requiring the prime minister to seek an extension to the Article 50 deadline
A bill from Labour MP Yvette Cooper, with the backing of Remainer Tory MPs, which also directs the prime minister to seek a deadline extension if a Brexit deal is not agreed by 26 February
An amendment by Labour MP Hilary Benn which asks MPs to take a non-binding vote on four options: reconsidering May's deal, leaving the EU with no deal, seeking to renegotiate the deal or holding another referendum
Some ministers are reportedly backing the proposals to block a no-deal Brexit, with the i newspaper and the Times saying that dozens could quit unless they are allowed a free vote on the issue.
The papers said that Work and Pensions Secretary Amber Rudd has warned May that up 40 ministers could resign.
'A proper say'
Last week MPs rejected the deal negotiated between the UK and EU on the terms of the UK's departure from the bloc by 432 votes to 202 - a majority of 230.
Outlining her proposed way forward on Monday, May refused to rule out a no-deal Brexit and insisted there was no majority in the House of Commons for another referendum.
But she promised Parliament a "proper say" in the next stage of negotiations on the future relationship between the UK and EU.
She also said she would conduct further talks on the Irish backstop plan, which is designed to prevent the need for a visible border and customs checks between Northern Ireland and the Irish Republic.
It means Northern Ireland staying aligned to some rules of the EU single market and effectively keeps the UK in the customs union until the UK and EU reach a lasting trade agreement.
The backstop is opposed by many Conservative MPs and the Democratic Unionist Party because they fear it could become permanent and because it means different rules for different parts of the UK.