Pro-European Conservative MPs could join forces with Labour to block the kind of Brexit Theresa May wants, a Tory rebel has warned the PM.
Anna Soubry claimed there would be a Commons majority against leaving the single market and customs union.
Labour's Chuka Umunna, appearing alongside Ms Soubry on the Andrew Marr show, agreed with her comments.
MPs have been promised a "meaningful vote" on the terms of Brexit before it happens in March next year.
"If this government doesn't get this right," said Ms Soubry, "the majority of members of parliament, putting their constituents first, will find themselves unable to vote for a withdrawal agreement."
Theresa May is set to deliver a major speech within the next three weeks outlining the future relationship Britain wants to have with the EU.
The prime minister has ruled out continued membership of the single market and customs union.
But Ms Soubry, one of 11 pro-European Conservative MPs who defeated the government in December on the right to get a vote on any final Brexit deal, said the PM's stance was a "huge mistake".
"Not only is it bad for our economy but it also fundamentally undermines the [Northern Ireland] peace process that was achieved and this is really important," she told Andrew Marr.
She said she wanted the UK to remain in the European Free Trade Area, like Norway, which would allow access to the single market without being a member of the EU.
Asked by Andrew Marr if they believed they had a majority in the House of Commons to defeat "the kind of Brexit the prime minister wants", Ms Soubry said: "If she's not careful, yes."
Mr Umunna said: "There is no majority in the House of Commons for us simply to jump off a cliff."
When Andrew Marr suggested to Ms Soubry that she was politically closer to Mr Umunna than she was to leading Brexiteer and Conservative colleague Jacob Rees-Mogg, she said: "I'm not denying that."
Asked if she thought Brexit would definitely happen, Ms Soubry said: "I genuinely don't know what is going to happen."
Responding to whether it might be stopped, she said: "Well I'll tell you who might stop it, and that's the people of this country.
"We won't stop it. It is the people. We gave the people a referendum to start this process."
Mr Umunna said he also backed another referendum on the terms of the Brexit deal - something his party leader Jeremy Corbyn has appeared to rule out.
He claimed the Labour leader - who last month rejected calls to attend a cross-party summit on avoiding a "hard Brexit" - was "open minded" about staying in the single market.
"I cannot conceive of circumstances where Labour MPs are marshalled to go through the lobby and vote against us staying in the customs union and the single market, with the likes of Jacob Rees-Mogg, Boris Johnson and Michael Gove," said Mr Umunna.
Both MPs insisted they were acting in the "national interest," which they said transcended party politics.
Labour's shadow chancellor John McDonnell said another Brexit referendum would cause divisions and a "better route" would be to have a general election.
"Better we have a general election. On the issue, and all the other issues, because you then have a wider debate as well," he told told ITV's Peston On Sunday.
Lib Dem leader Sir Vince Cable, who is campaigning for another referendum, said: "It is good to see cross-party cooperation between Tory and Labour rebels."
He said he was "optimistic that the rebellions in both Tory and Labour parties will spread in coming weeks", and that his party was working with them in the House of Lords.