She later announced the vote would go forward in the week beginning January 14.
Led by former Labour minister Yvette Cooper, the group has tabled two amendments to the Finance Bill that would paralyse the government unless May wins her vote, the Times reported.
But parliamentary opposition to her deal remains fierce, with the main sticking point being the safety net "backstop" measure - which would guarantee no hard border is erected on the island of Ireland in the event that post-Brexit trade negotiations between the United Kingdom and the bloc prove unsuccessful.
May's withdrawal agreement has found opposition from Brexiteers resulting in the prime minister postponing the House of Commons vote before Christmas in face of certain defeat - mainly over the issue of the Irish backstop which could see Northern Ireland locked into regulatory alignment with the bloc after the transition period, should London and Brussels not strike a deal, in order to stop a so-called "hard border" with European Union member state Republic of Ireland.
May has already delayed the vote once, in December, when it became clear she would lose unless extra reassurances from the European Union were agreed.
As the parliamentary debate on her deal is due to begin next week, on 9 January.
May also did not directly respond, when asked, if she was leading the country toward a no-deal Brexit.
"The danger there is that we end up with no Brexit at all", May added, also dismissing calls from Brexit opponents to hold a second referendum.
Prominent Brexiteer Peter Bone said a no-deal scenario was the only way to guarantee the United Kingdom actually leaves the EU.
According to The Guardian, in the interview, May repeatedly sidestepped issues about whether she would keep putting the deal back to MPs if it got rebuffed.
Ms Thornberry said her party would be happy to "go back to the people" if it won power at a snap general election but failed to get its own Brexit plans through.
The survey of more than 25,000 people, commissioned by the People's Vote campaign, found that 75 per cent of Labour voters supported the idea of another referendum.
"We will be holding the vote", May insisted.
Sir Vince Cable said: 'The time has now come for MPs to assert their authority by making it impossible for the government to collect crucial taxes if they do pursue a damaging no deal'.
Reports this weekend suggest that Downing Street are planning to put the deal before parliament up to 30 times in an attempt to bludgeon MPs into backing it in order to prevent a no-deal Brexit.
"I don't think anybody can say exactly what will happen in terms of the reaction we will see in Parliament".