Arch-Eurosceptic Jacob Rees-Mogg hinted that he might now be forced to back British Prime Minister Theresa May's deal if the alternative was no Brexit at all.
On his Conservative home podcast, the European Research Group chairman said: "The Prime Minister will not deliver a no-deal Brexit."
Asked if that meant the options were now "deal or potentially no Brexit", he said: "That, I think, becomes the choice eventually.
"Whether we are there yet is another matter, but I have always thought that no-deal is better than Mrs May's deal, but Mrs May's deal is better than not leaving at all."
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He added that "leaving the European Union, even leaving it inadequately and having work to do afterwards is better than not leaving at all".
Brexit may now need to be viewed as "a process rather than an event".
It was, he said, a "process of unravelling and diverging which will take time".
Mrs May has been warned she is "playing with fire" if she ignores parliament after MPs adopted a cross-party Brexit amendment that allowed parliament to seize control of the House of Commons agenda.
Three junior ministers resigned last night in order to defy the government line.
Mrs May responded by saying her government would not be bound by the results of the so-called indicative votes.
Former Conservative minister Michael Heseltine said ignoring parliament would be dangerous for Mrs May.
"I think she is playing with fire when she says she is not going to take any notice of what the House of Commons says," he told BBC radio.
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"There is no doubt at all that public opinion is moving, quite significantly now, appalled at what has happened and the events that we see and apprehensive of the fact that we haven't even begun to negotiate the real deal."
MPs have called on Mrs May to heed whatever alternative Brexit strategy they can settle on after they attempted to break the impasse by taking control of the process in parliament.
The government insisted the deal Mrs May agreed with the European Union in November after more than two years of negotiation remained the only way forward for taking Britain out of the EU.
That deal has been voted down twice in parliament.
Mrs May hopes MPs who want an abrupt no-deal Brexit will now fall in behind her or risk seeing a long delay which could end up with Britain remaining closer to the EU or not leaving at all.
Labour MP Hilary Benn said: "If parliament is able to come up with a way forward, the question is whether the government is prepared to compromise."
He conceded that the government could ignore the indicative votes and press on with Mrs May's plan.
"That is indeed possible, but it is not an argument for not trying because we are in a complete mess. The government is in chaos," he said.
Possible options to be considered include Mrs May's deal, a no-deal Brexit, another referendum, revoking Article 50, a free trade agreement with a customs union, and staying in the EU's single market.
Conservative MP Steve Brine, who quit as a junior health minister yesterday, said parliament might be able to break the deadlock.
"The bottom line is that something has got to change," he said.
"We are stuck in this maddening impasse where we go round and round in circles, something has to move us forward. The House of Commons is not going to come up with something completely crazy."
Health Minister Matt Hancock said Mrs May's deal remained the only option on the table and ousting the prime minister would not help resolve the impasse.
Mrs May has not ruled out bringing back her deal for a third time this week, possibly on Thursday.
"Changing the party leader doesn't change anything. It doesn't change the arithmetic in parliament and also it would be a huge distraction," Mr Hancock said.
Last week, the EU agreed to delay Britain's original 29 March departure date because of the deadlock.
Now, it will leave the EU on 22 May if Mrs May's deal is approved this week. If not, it will have until 12 April to outline its plans.
Nearly three years after Britons voted 52-48% to leave in the 2016 EU membership referendum, and three days before Britain was supposed to leave the bloc, the outlook for Brexit remains up in the air.
Brexit minister Stephen Barclay said on Sunday if parliament took control of the Brexit process, a snap election, which the Labour Party would likely back, could follow.
Additional reporting PA
