Part of Mrs May's Brexit deal includes plans for an "ambitious, wide-ranging and balanced" trade agreement, but the text is not legally binding.
Danielle Haralambous, a United Kingdom analyst at the EIU, said: "Time is simply running out, and we're at a stage where Brexit can probably only happen in late March now in the unlikely event that parliament approves Mrs May's deal on 15 January, or if parliament supports leaving without a deal".
"What is more likely if this deal is rejected is that we have the risk of Brexit paralysis and when that happens no one knows what might happen and the big risk, and what people worry about, is that we don't actually deliver what people voted for", Jeremy Hunt told Sky News on Friday.
Britain is unlikely to leave the European Union on March 29, the Economist Intelligence Unit has predicted.The forecasting group said it expects the PM will lose the critical "meaningful vote" on her Brexit deal on Tuesday, and the government will then be forced to request an extension to Article 50.The EIU believes Brussels will agree to an extension, meaning Britain will remain in the trade bloc beyond the planned exit date.
MPs on all sides of the Brexit debate fear the so-called Northern Ireland backstop could leave Britain tied to the European Union indefinitely.
The Cabinet ministers were speaking as MPs prepared for the third day of debate in the House of Commons ahead of next Tuesday's crunch vote, with Home Secretary Sajid Javid opening proceedings which are expected to be dominated by the issue of migration.
More than 100 Conservative MPs have already declared their intention to vote against May's deal.
That could open the way for several different outcomes, ranging from a so-called "managed no-deal" exit to another referendum.
The PM has said failing to deliver on the result of the 2016 referendum would be "unforgivable" and a "catastrophe" for democracy.
"I think that is something that we would regret for many, many generations".
A senior government official on Sunday described the plan as extremely concerning, since if it succeeds lawmakers would gain control over not just Brexit legislation but all legislation.
'When you turned out to vote in the referendum, you did so because you wanted your voice to be heard, ' she said.
It was not possible for the minority Tory administration to control what happened in parliament, and Speaker John Bercow had shown that he was "willing to frustrate the government at every opportunity", he said.
Mrs May faced further opposition to her deal from her former Brexit secretary Dominic Raab.
Lawmakers are set to vote on May's Brexit deal on Tuesday, after she shelved plans for a vote in December when it became clear that not enough lawmakers from her own party or others would back the deal she agreed with Brussels.
The prime minister will make this plea: "I ask MPs to consider the consequences of their actions on the faith of the British people in our democracy".
Pressed for a third time by interviewer Justin Webb on whether she would quit if Mrs May went for the no-deal option, Ms Rudd cut him short by saying: "Thank you very much, Justin".