Senior Brexiteer minister Liam Fox says he believes 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
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".
The vote on the withdrawal agreement is planned for the third week of January.
The UK is due to leave the EU on 29 March 2019.
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 May to cut short MPs' Christmas break - they are due back in the Commons on 7 January - to
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 per cent 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 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.