Remain-backing MPs believe they will get a chance to send Theresa May back to the negotiating table if they don’t like the final Brexit deal, after comments by David Davis.
The Brexit secretary suggested MPs would be allowed to amend a motion on the deal in the autumn.
Downing Street has said the vote will be a “take it or leave it” choice.
But the Brexit secretary suggested that might not be the case in evidence to a select committee.
Mr Davis restated the government’s promises of a “meaningful vote” in the autumn, in evidence to the Exiting the EU committee.
But he confirmed that MPs and peers were likely at that stage to be presented with “a political declaration rather than a treaty draft”.
Asked by the committee’s Labour chairman Hillary Benn whether the motion would be amendable, the Brexit secretary replied: “If you can tell me how to write an unamendable motion, I will take a tutorial.”
Pressed on whether the government would regard the outcome of the vote as binding, Mr Davis said: “The government is unlikely to put a vote to the House which it doesn’t intend to take properly seriously. If the House rejects the proposed negotiation, that negotiation will fall.”
Labour MP Stephen Kinnock asked Mr Davis what would happen if MPs amended the government motion on the deal and voted to send ministers back to Brussels to negotiate a different deal.
Mr Davis told the committee: “I’m not going to speculate on amendments that have not even yet been laid, let alone been passed by the House.”
Mr Kinnock replied: “Surely you must appreciate the risk of us heading towards a constitutional crisis here?
“And surely it’s the responsibility of the government to have scenarios in mind so that it is ready to respond when the House does vote?”
Mr Davis responded: “I’m not going to give advice on how to create circumstances which may undermine the government’s negotiating position.
“I’m not entirely sure how much force a government sent back with its tail between its legs by Parliament would have in such a negotiation.”
Remain-supporting Labour MP Pat MacFadden, from the Open Britain campaign against a “hard and destructive Brexit”, told the BBC Mr Davis’s words gave hope to those campaigning for a referendum on the final deal, as Mr Davis had refused to “repeat his previous assertion that that would be the end of the matter and we’d be leaving the EU with no deal in place”.
He said it would allow MPs, for example, to demand more time or to delay the article Article 50 process of leaving.
Mr Davis also told the committee he expects Parliament to “uphold” the government’s policy of leaving the customs union.
The Brexit secretary told MPs he always “respected” the wishes of Parliament, even when they defied ministers, but he believed they would not in this case.
MPs will hold a non-binding vote on the issue on Thursday after the Lords voted for some form of future customs union.
With Labour, the Lib Dems and the SNP, plus a handful of Tories, in favour of remaining in some form of customs union after the UK leaves, the government is at risk of potential defeat when the defining vote is held next month.
While the UK would remain a “de facto” member of the customs union during a 20-month transition period after Brexit, Mr Davis told the Commons Brexit select committee that there were “huge competitive advantages” to leaving in terms of boosting the UK’s share of global trade.
He said he hoped to get off to a “racing start” by implementing new trade deals quickly with countries like Canada after December 2020 – when the transition period will end.
Mr Davis also rejected reports that the EU had dismissed out of hand the UK’s solutions for avoiding a hard border on the island of Ireland.
It was suggested last week that EU officials believe neither free trade nor technological solutions are feasible and Northern Ireland will have to remain in full regulatory alignment in many areas with the Republic of Ireland – the so-called “backstop option”.
Mr Davis, who visited Northern Ireland last week, said this last outcome was “unacceptable – because it starts a process of effectively breaking up the UK”.
He said it was seen by all concerned as the “least most desirable outcome” – or what he described as a “reserve parachute” if all else failed – and far more preferable was to settle it through a comprehensive trade deal.
Warning against “artificial timetables”, he rejected claims the UK was running out of time, pointing out that Irish prime minister Leo Varadkar had said a workable deal by October was more important than any deal this summer.
But speaking in the Irish Parliament, Mr Varadkar said he wanted to see “sufficient or significant progress” on the issue by the time EU leaders gather for their next summit in June.