Senior Brexiteer minister Liam Fox says there is a 50-50 chance the UK will not leave the EU on 29 March if MPs reject Theresa May's Brexit deal next month.
The international trade secretary told the Sunday Times it would only be "100% certain" if MPs back the deal.
He said if the deal is rejected, that "would shatter the bond of trust between the electorate and Parliament".
MPs are due to vote on the withdrawal agreement in January, with the UK scheduled to leave the EU on 29 March.
The agreement negotiated by Mrs May with the EU - which sets the terms of the UK's exit and a declaration on future relations - will only come into force with a majority backing in Parliament.
The Commons vote was due to be held on 11 December but the PM postponed it once it became clear it would be defeated by a large margin.
Labour leader Jeremy Corbyn this week urged Mrs May to cut short MPs' Christmas break - they are due back in the Commons on 7 January - to allow for an earlier vote.
Mr Fox has warned fellow MPs that failure to pass the deal would be "incendiary" and said it was "a matter of honour" for them to support the PM.
He said: "What you can be sure of is that if we vote for the prime minister's deal then it's 100% certain that we will leave on 29 March.
"If we do not vote for that, I'm not sure I would give it much more than 50-50.
"And, for me, that would induce a sense that we had betrayed the people that had voted in the referendum."
Liberal Democrat MP Layla Moran, a leading supporter of the campaign for another referendum, said: "The only thing that is shattering the bond of trust between electorate and Parliament is the refusal of ministers like Liam Fox to trust people with the final say on Brexit."
If Mrs May's deal is rejected, the default position is for the UK to leave in March unless the government seeks to extend the Article 50 negotiating process or Parliament intervenes to stop it happening.
European Commission President Jean-Claude Juncker has urged the UK to "get your act together and then tell us what it is you want" for Brexit.
Speaking to the German newspaper Welt am Sonntag, he said it was "unreasonable" for parts of the British public to expect Brussels to solve "British problems".
Mr Juncker also rejected the idea that the EU wanted to keep the UK in the EU "by all possible means" and suggested the majority of MPs "deeply distrust" the EU and Theresa May.