Former Chancellor George Osborne has said delaying the UK's exit from the EU is now the "most likely" option.
The UK has to choose between no deal - which he compared to Russian roulette - or no Brexit for now, he told the BBC.
But Theresa May says the best option is to approve her withdrawal agreement, which MPs rejected last week.
And International Trade Secretary Liam Fox told the BBC that if MPs blocked Brexit it could have "calamitous" and "unforeseen consequences".
Under current law, the UK will exit the EU on 29 March, whether or not a deal has been struck. The decision to leave was taken by 52% to 48% in a referendum in June 2016. Mr Osborne, now a newspaper editor, was chancellor and a key Remain campaigner at the time.
Speaking to BBC business editor Simon Jack in Davos, Mr Osborne said that the prospect of no deal meant "the gun is held to the British economy's head".
"Russian roulette is a game which you should never play because there's a one-in-six chance that the bullet goes into your head," he said.
Mr Osborne, who was sacked by Mrs May when she became prime minister after the referendum, said his successor Philip Hammond had "sensibly" told businesses that leaving without a deal was not a possibility.
"But we now need to hear it from the British prime minister," he said.
Mr Osborne said that although there might be a majority in Parliament to prevent no deal, it was not clear how MPs would achieve it.
Shadow chancellor John McDonnell told the BBC's Newsnight that it was "highly likely" the party would back an amendment put forward by Labour MP Yvette Cooper, with support from MPs in other parties.
It would give time for a bill to suspend the Article 50 process for leaving the EU if a new deal has not been agreed with Brussels by the end of February.
"I think it's increasingly likely already that we'll have to take that option because the government has run the clock down," Mr McDonnell said.
It is one of several alternative plans by MPs that will be put forward when Mrs May returns to the Commons on 29 January to set out her own proposed next steps.
Among the MPs' plans are to consider a range of options over six full days in Parliament before the March deadline or hold a representative "Citizens' Assembly" to give the public more say.
Another proposal seeks to win over some opponents of the prime minister's deal by insisting on "an expiry date to the backstop", the "insurance policy" intended to avoid a hard border on the island of Ireland.
The backstop is opposed by some Conservative MPs and Northern Ireland's Democratic Unionist Party because it could mean keeping the UK in a customs union with the EU indefinitely and having different rules for different parts of the UK.
But the Taoiseach (Irish prime minister) Leo Varadkar said he could not give up the formal guarantee of the backstop "for a promise that it will be all right on the night".
The European Commission also warned that it was "obvious" that a no-deal Brexit would mean a hard border in Ireland.
Scottish First Minister Nicola Sturgeon, who is meeting Mrs May for talks on Wednesday, said she supports seeking an extension to the Brexit deadline.
Meanwhile, Dyson, the company founded by vocal Brexit advocate Sir James Dyson, has announced it is moving headquarters to Singapore.
However, chief executive Jim Rowan said the decision was prompted by growing opportunities in Asia rather than by Brexit.