Breaking the rule of refusing to acknowledge the necessity for a plan B to May's plan, Amber Rudd suggested that a Norway-style deal, which would keep Britain tied to large parts of European law, "seems plausible not just in terms of the country but in terms of where the MPs are".
A defeat would sink the agreement, leaving the United Kingdom facing a messy "no-deal" Brexit, and could topple May and her government.
Will Quince, a ministerial aide to Defence Secretary Gavin Williamson, hit out at the backstop plan to avoid a hard border with Ireland, saying it could result in the United Kingdom being "tied to the negotiating table for years, until we agree to anything in desperation" to get out of the situation.
Mrs May was warned by critics that she could be forced to stand down as Prime Minister if her Brexit deal is defeated in the Commons next week.
"We voted to leave, we should deliver on leaving and we can do it in a way that works", she said.
According to the Esher and Walton MP - who spent five months as the secretary of state leading Brexit negotiations - United Kingdom officials were not firm enough when discussing the backstop with the EU.
Prime Minister Theresa May was back in United Kingdom parliament for day three of a debate to sell her Brexit deal to ministers ahead of a key vote next week.
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In an interview with Political Editor Robert, Mr Corbyn said a second vote could be held while still respecting the outcome of the June 2016 referendum.
Today pro and anti Brexit campaigners were out in force - in separate demonstrations, but united against the PM's deal.
May said rejecting her deal would also risk the opposition Labour Party getting into power.
She added: "If people asked me, then of course you'd give it serious concern and do it if people asked me".
Several MPs, including the parliamentary leader of the Northern Irish DUP Nigel Dodds, former Brexit minister Dominic Raab and former work and pensions minister Esther McVey called for May to renegotiate with Brussels.
"We have a leader of the Opposition who thinks of nothing but attempting to bring about a general election, no matter what the cost to the country".
Preparations should also be stepped up for a no-deal Brexit, he said.
Former Cabinet minister Esther McVey, who resigned over the Brexit deal, said Sunday that May must immediately return to the European Union and "get a better deal" if she loses Tuesday's vote.
Rudd, who backs May's Brexit deal, said "anything could happen" - including a second referendum - if the government is defeated in Parliament, and predicted a chaotic period.