While 49 percent of those surveyed believe that a no-deal Brexit will result in an economic catastrophe for the country, 33 percent would back it.
If she hasn't brought a new deal to Parliament by February 27, she'll say there will then be another opportunity to vote, Communities Secretary James Brokenshire said in a BBC interview.
The former PM said crashing out of the European Union would inevitably lead to a "really hard border" on the island of Ireland and cause a huge split within the UK. Both London and Brussels are therefore concerned over the possibility of a no-deal Brexit.
He said that Mrs May intends to return to Parliament after the 21-22 March European summit - with just one week before Brexit - and offer MPs a choice between her deal and a no-deal Brexit.
May is set to address parliament about the state of negotiations by Wednesday at the latest, with MPs set to vote on Thursday on how to proceed. The new pledge would be for a repeat of this process by February 27.
Mrs May has been seeking legally binding changes to the plans for avoiding a hard border in Ireland.
British Prime Minister Theresa May will pledge this week to give parliament another chance to voice their opinions on Brexit by February 27 as she tries to buy more time to negotiate a new deal with the European Union.
After talks with Brussels this week Mrs May said that she was determined to deliver Brexit on time ahead of the March 29 deadline.
Labour leader Jeremy Corbyn has written to the Prime Minister setting out five demands that would have to be met for his MPs to support a deal, including a permanent customs union and close alignment with the single market.
"Or the only way to break the impasse is to have a public vote, and that remains our policy".
"We shouldn't be put in a position where the clock is run down and the prime minister says it's either my deal or even worse", Labour's Brexit pointman Keir Starmer told The Sunday Times.
Asked by Sky News if she could stay in office if that became government policy, Tuss said: "I absolutely do not think that should be our policy".