But it is hard for a prime minister with limited support in her party, to argue against giving parliament the final say.
Using the example of there being another referendum where Remain narrowly wins, he said: "Let me tell you that if there is another referendum, which I don't think there will be, people like me will be immediately demanding it is best of three".
At the same time, May's Chief of Staff Gavin Barwell has said that holding a second referendum was "the only way forward".
Underscoring the acrimony in the United Kingdom over Brexit, Mrs May and former prime minister Tony Blair of the Labour Party traded jibes in the media.
"It is perfectly clear neither the British people nor their Parliament will unite behind the Prime Minister's deal".
If parliament fails to approve the text, Britain will crash out of the European Union regardless - a prospect that experts warn could lead to serious trade disruption and trigger a financial crisis.
The idea of a second referendum is gaining traction among those who hope it would stop the United Kingdom leaving the bloc, and those who see it as a threat that will bring Brexiteers behind May's plan.
"No, a second referendum would be divisive", British education minister Damian Hinds said.
I learned to walk again, says Arsenal captain Laurent Koscielny
Laurent Koscielny has revealed that he had to learn how to walk again after he underwent achilles surgery in May. Emery was similarly pleased with his return, saying: "Today is another step for him and for us".
Trevor Ariza trade to Washington Wizards from Phoenix Suns
Keep in mind nothing can be done until December 15, when free agents who signed this past summer are eligible to be traded. However, the deal is now reportedly in jeopardy as there is some confusion over which players were included in the deal.
Real Madrid coach, defender praise family atmosphere at Spanish club
Vinicius Junior at 18 years and 152 days is the third youngest player to ever start a Champions League match for Real Madrid . Ronaldo De Lima said it was not coincidence that Cristiano Ronaldo was still on top of his game at 33 years of age.
Theresa May is talking about a second referendum today; she will tell MPs that it would do "irreparable damage" to our democracy.
Blair added: "I have always said, and did again in my speech on Friday in London, that I personally sympathise with the PM's heavy burden in doing her job".
International Trade Secretary Liam Fox echoed a chorus of senior Scottish Tory warnings that a second European Union referendum would give Scottish National Party leader Nicola Sturgeon the leverage for another independence vote.
She went to Brussels at the end of a week in which she delayed the Commons vote on her Brexit deal, admitting it would be rejected by a significant margin, and then went on to survive a vote of no confidence in her leadership by Conservative MPs by 200 votes to 117.
Former British Prime Minister Tony Blair has found himself in a public spat with Theresa May, saying her Brexit plan isn't in the national interest.
The Labour Party, which is under pressure from smaller opposition parties to propose a motion of no confidence against the government this week, said on Sunday it would seek to force May to bring the deal back to Parliament for a vote before Christmas.
But EU leaders told her the negotiated withdrawal agreement was "not open for renegotiation", although some clarification was possible.
But Labour leader Jeremy Corbyn said her deal was now "dead in the water" and the prime minister had "utterly failed in her attempts to deliver any meaningful changes".
As the prime minister faces incoming fire over her return from Brussels last week empty-handed, and the clock ticking down to exit day without an apparent plan B, does she protest too much about another vote? "Something that people do in the real world all the time, but which seems so alien in our political culture - to engage with others", she said.