MPs are due to vote on whether to back Mrs May's Brexit plan next week.
She later announced the vote would go forward in the week beginning January 14.
Following the cancelled vote, May survived a leadership challenge triggered by disgruntled Eurosceptics in her party and has been back to Brussels to try and get additional reassurances about the so-called Irish backstop which was a major sticking point in opposition to the deal.
European Union officials have insisted that the withdrawal agreement can't be renegotiated, although they also stressed that the backstop was meant only as a temporary measure of last resort.
The Prime Minister warned critics from both sides of the Brexit divide that they risked damaging the economy and trust in democracy by opposing her plan.
"The backstop remains the poison which makes any vote for the Withdrawal Agreement so toxic. The coming days will show if this Government is made of the right stuff", the Democratic Unionist Party Deputy Leader Nigel Dodds said as quoted by the Irish Examiner.
London Mayor Sadiq Khan said the Brexit process should be immediately halted if Mrs May's deal is rejected by Parliament - with the decision put back to the people.
"We are pretty much where we were before Christmas, with the proviso that there's less time left".
MPs including Yvette Cooper and Nicky Morgan tabled an amendment to the finance bill that would allow ministers to implement tax changes after Brexit only if parliament has backed a deal, endorsed a no-deal departure or during an extension to Article 50.
But she added: "If Parliament says 'This is just nonsense, this is no better than Theresa May's [deal],' we will put our hands up to that".
But she admitted she had no way of knowing what might happen if MPs rejected her deal, adding that the country would be in uncharted territory.
In a letter published by United Kingdom newspaper the Mail on Sunday, May warned critics of her departure plan risk damaging Britain's democracy and weakening its economy by opposing her deal.
She also alleged her deal was the only one that respects the UK's 2016 referendum result, in which 52 percent of Britons voted to leave the EU.
Amid the uncertainty over Britain's next steps - which range from leaving without a deal to not leaving at all - a poll showed more Britons want to remain a member of the European Union than leave, and voters want to make the final decision themselves.
When the undecided and those who refused to answer were removed from the sample, the split was 54-46 in favour of remaining.
The poll of more than 25,000 voters was commissioned by the People's Vote campaign, which is spearheading an increasingly vocal push for a second referendum on Brexit. Removing those who are undecided, the split was 53 per cent in favour of another referendum and 47 per cent against.
But Mr Corbyn would be under pressure back another referendum if this proved impossible, with a YouGov poll suggesting support for another vote is high among Labour supporters.
"It's very hard to achieve - there isn't a majority in parliament for it ..."
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