Parliament will not accept a no-deal Brexit, Cabinet minister Amber Rudd has said.
And Ms Rudd warned that Brexit may not go ahead if MPs reject Theresa May's withdrawal agreement in a House of Commons vote expected next month.
The Work and Pensions Secretary was speaking as Mrs May came under pressure from Tory Brexiteers to secure further concessions from the EU in a top-level Brussels meeting on Wednesday evening
The Prime Minister will meet European Commission president Jean-Claude Juncker for talks ahead of the special EU Brexit summit on Sunday at which the remaining 27 member states are expected to approve her plan.
She is under pressure to make changes to the Northern Irish backstop contained in the Brexit divorce agreement, making it clear how the UK can exit the controversial arrangement.
With large numbers of Conservatives, as well as the 10 DUP MPs who prop up Mrs May's administration in the Commons, threatening to vote down her deal, the Prime Minister has repeatedly warned that the alternative is a damaging no-deal Brexit.
But Ms Rudd told BBC Radio 4's Today programme: "It is my view that the House of Commons will stop no-deal.
"There isn't a majority in the House of Commons to allow that to take place."
The minister, a former Remain campaigner who replaced Leave-backing Esther McVey in the Cabinet following her resignation last week, added: "If it doesn't get through, anything could happen.
"The Brexiteers may lose their Brexit."
Ms Rudd made clear that she expected MPs to rally behind Mrs May's proposals, telling Today: "I don't think we are looking at another referendum.
"I think people will take a careful look over the abyss - MPs of all parties - and consider whether they think it is in the best interests of the whole country.
"I think the likelihood is, despite what people say, that the Withdrawal Agreement will get through."
But her comments were seized upon by Labour, whose shadow chancellor John McDonnell told an event at Reuters in London that there was "an overwhelming majority opposing anything that smacks of being no-deal".
Shadow Brexit secretary Sir Keir Starmer said: "Amber Rudd seems to have ignored Number 10's spin by admitting that Parliament would stop a no-deal Brexit.
"If the Prime Minister's deal is rejected then MPs will not sit back and allow us to crash out of the EU without an agreement.
"Parliament will take back control.
"After these comments from Amber Rudd, it's time for the Government to drop the false choice between a bad deal and no deal, and to come forward with a plan that can command the majority support of Parliament."
Scottish First Minister Nicola Sturgeon said: "Amber Rudd exposes the falsity of the PM's tactics - it is not a choice between her bad deal or no deal. There are better alternatives."
The People's Vote campaign for a second referendum said Ms Rudd had "torpedoed the PM's threat of no deal".
Labour MP and People's Vote supporter Tulip Siddiq said: "The threat of no deal was always to try and scare MPs into backing her - now one of the Prime Minister's key remaining allies has blown that fallacy apart, it is time we had a final say.
"We must have a people's vote on this bad Brexit deal."
Ms Rudd's comments will increase Mrs May's difficulties at what was already expected to be an awkward session of Prime Minister's Questions, amid mounting evidence of tensions between Mrs May and the Democratic Unionist Party over the Brexit deal.
The Government caved in to a series of opposition amendments to its Budget-enacting Finance Bill in the latest sign that the DUP's MPs would not support Mrs May's minority administration.
Mrs May's talks with Mr Juncker follow confirmation from Number 10 that the Government will look at potential technological solutions to keep the Irish border open.
The Prime Minister's official spokesman confirmed that references in last week's draft agreement to "alternative arrangements" for the border could involve technical measures of the kind previously promoted as the "maximum facilitation" solution, or Max Fac.
Brexiteer ministers want her to press for clarity on how the UK can avoid or end the use of the backstop, which would require the whole UK to be in a single customs territory with the EU and force Northern Ireland to align with many of Brussels' single market rules after 2020, unless an alternative is found.
A Brexit-backing minister said that the negotiation process was "not over until it's over" and it was now a case of "who blinks first" as Brussels did not want either the backstop to be implemented or the prospect of the UK crashing out without a deal.
German Chancellor Angela Merkel set her face against any change to the deal to give the UK the independent right to end the backstop.
Mrs Merkel told the German Parliament: "We have placed value, and I think this is right, on the fact that Britain cannot decide unilaterally when it ends the state of the customs union, but that Britain must decide this together with the EU."
Mrs Merkel said that Germany will back the proposed withdrawal agreement at Sunday's summit, and hoped that objections raised by Spain to the treatment of Gibraltar would be "solved" by this time.
Influential Conservative backbencher Damian Collins, the chairman of the Commons Culture Committee, said that he could not back Mrs May's deal as it stands and suggested there should be an election or second referendum if the country is facing a no-deal Brexit.
"If we couldn't get an agreement and we were stuck in a situation where it was a deal we don't want, or the cliff edge... I don't think as Parliament we could just stand back and watch the country fall off the edge of a cliff without asking the people whether that was the step they wanted to take," Mr Collins told Today.
Brussels has indicated that the withdrawal agreement, setting out the terms of the UK's divorce from the bloc, will not be rewritten - although work is ongoing to flesh out the political declaration on the future UK-EU relationship.