And while Mrs May has publicly ruled out the possibility of a second referendum, Labour has said it could support one if the Prime Minister's deal is voted down.
Sky News understands Mrs May would struggle to delay the vote because the debate leading up to it has already started - meaning she would need to win another vote adding an amendment to push it back.
The Scottish National Party's leader in Westminster, Ian Blackford, called on Mrs May to take responsibility for "concealing the facts on her Brexit deal" from MPs and the public.
But Sir Graham Brady, chairman of the powerful 1922 committee of Conservative backbenchers, has told her to think again as more than 100 Tory MPs have publicly slammed the deal - with many angry the United Kingdom could be locked into the Northern Ireland backstop indefinitely.
Allies of the prime minister have looked at the potential for a People's Vote which would be between remaining in the European Union or her deal, which they believe could be won if there is a uarantee to end freedom of movement.
"We believe ours was a fair and appropriate format for those taking part and, crucially, for our audiences around the country, and it is a shame we will not be able to bring them this programme", the BBC said in a statement.
Theresa May has rejected a plea from some in her cabinet to postpone the vote on the withdrawal bill but has offered concessions to parliament on the contentious issue of the backstop arrangement for avoiding an Irish border.
Brexit: What do the Government's legal position papers say?
"It is unthinkable that the government tried to keep this information from Parliament - and indeed the public - before next week's vote", he said, making a reference to the crucial vote on the Brexit deal set for next Tuesday.
"(It) would mean an immediate and probably indefinite loss of some security capability which, despite our best efforts, would likely cause some operational disruption when we leave", he said.
May has repeatedly said if lawmakers reject her deal with Brussels, which would see Britain exit the European Union on March 29 with continued close ties, the only alternatives are leaving without a deal or reversing Brexit.
Mr Javid warned that "no matter how effectively" the government prepares for a no-deal Brexit, there would be "consequences" for the UK's security.
Led by Hugo Swire, the alternative plan would give MPs the chance to vote to extend the transition period at the end of 2022 - rather than falling into the backstop.
Bob has previously said he will support the Prime Minister's deal to secure Brexit.
During the first two days of debate, at least 15 of May's own lawmakers explicitly said they intend to vote against the deal, and British media have speculated that as many as 100 could ultimately rebel.
Shadow Brexit secretary Sir Keir Starmer said that the 33-paragraph document revealed "the central weaknesses in the Government's deal".
Rapid Test for Cancer Developed by Researchers
Scientists developed a so-called "universal cancer test " that can detect traces of the disease in the bloodstream of a patient. The test has a sensitivity of about 90%, and this means that it would be able to detect about 90 cases of cancer from 100.