Some cabinet ministers now believe that May is so wedded to her Brexit deal that her only method of gaining approval will be through another referendum - and that the arguments for a second vote are emerging as stronger than those for a soft Brexit.
Other ministers - including Work and Pensions Secretary Amber Rudd - have suggested that a Norway-plus deal keeping the United Kingdom in the single market and a customs union could be a "plausible" alternative if Mrs May's plan is rejected.
Ms Rudd predicted a "chaotic" period if the Government is defeated.
With her own future in the balance, May insists her deal, laboriously negotiated with the European Union over many months, is the only one on the table and that the alternatives are a painful "no-deal" exit from the European Union or possibly no Brexit at all.
Pro-Brexit lawmakers say the deal keeps Britain bound too closely to the European Union, while pro-EU politicians say it erects barriers between the United Kingdom and its biggest trading partner and leaves many details of the future relationship undecided.
"I can't understand the hysteria around a People's Vote if you believe in what you are trying to propose", she said.
Theresa May is battling to save her Brexit deal and maintain her grip on power ahead of Tuesday's Commons showdown.
Brexit Secretary Stephen Barclay insisted that the vote would still go ahead on Tuesday amid speculation Mrs May might be forced to delay the vote in a last-ditch effort to avoid defeat.
She told her MPs: "'If you want Brexit, make sure you get it, and that's about this deal".
Rudd told The Times newspaper in an interview her own preferred option, if May's deal failed, was the "Norway Plus" model, adding it "seems plausible not just in terms of the country but in terms of where the MPs are".
Of the 60 Conservative MPs in the Anglia region, 20 are on the government payroll as ministers or whips and so would be expected to support the deal or resign.
Supporting the withdrawal agreement secured by the PM, Ms Rudd said: "I think this is the right deal for the country". Far from healing divisions at home and allowing us to move on, this deal would carve out the battle lines of the future.
Hilary Benn, chair of the committee, said the government had "refused to face up to the hard choices confronting us".
"But it's better than the governments proposal, but it would not be accepted politically in the UK".
"The risk for those who say simply go back and ask again, the risk is that isn't necessarily a one way street, the French the Spanish and others will turn round, if we seek to reopen the negotiation, and ask for more", he added.
But the report says this would "result in immediate barriers to UK-EU trade in goods and services".
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