While a large majority of party members, according to polling, want Corbyn to actively seek a new referendum, the Labour leader has previously said it is more likely he would push to take the United Kingdom out of Europe with a different deal.
Meanwhile, Work and Pensions Secretary Amber Rudd declined three times to say whether she would resign if a no-deal Brexit took place.
However, when the BBC asked what happens if the deal is defeated, Barclay said he suspected the Commons would support something "along the lines of this deal" but did not speculate on whether the government had a Brexit "plan B" lined up.
Mrs May said: "When you turned out to vote in the referendum, you did so because you wanted your voice to be heard".
Described as "a very British coup", the plan would see May lose control of parliamentary business to MPs, threatening her ability to govern, the newspaper said.
"Doing so would be a catastrophic and unforgivable breach of trust in our democracy", May said.
It said Downing Street was "extremely concerned" about the possibility, which could see lawmakers then delay Brexit through new legislation.
"So my message to Parliament this weekend is simple: It is time to forget the games and do what is right for our country". "Projectfear? Project terror? Extremism more likely if we get failed Brexit which leads to lower living standards and less money for services".
Meanwhile, Work and Pensions Secretary Amber Rudd said she is "committed" to ensuring that the United Kingdom does not leave without a deal.
Elsewhere, it emerged that Speaker John Bercow met Tory remain rebel Dominic Grieve on Tuesday, the day before his controversial decision to allow MPs a vote on Mr Grieve's amendment to the timetable of the Brexit deal.
And the prime minister made efforts to reach out to Labour and the unions in an 11th-hour bid to salvage a vote which she is expected to lose by a wide margin.
But he told Marr: "My own view is that I would rather get a negotiated deal now, if we can, to stop the danger of a no deal exit from the European Union on the 29th March, which would be catastrophic".
Mr Halfon is one of those who plans to vote against the prime minister Brexit deal in the House of Commons next week, saying: "I don't like voting against the prime minister" but that he feels he would be breaking a promise to his constituents to honour the Brexit result if not.