"When I say if this deal does not pass we would truly be in uncharted waters, I hope people understand this is what I genuinely believe and fear could happen", she was quoted as saying.
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.
Ms Rudd, who campaigned for Remain in 2016, also refused to rule out a further referendum, despite the prime minister doing so on multiple occasions.
She accused Labour leader Jeremy Corbyn of thinking of "nothing but attempting to bring about a general election, no matter what the cost to the country" and, in a warning to Tory rebels, said: "I believe Jeremy Corbyn getting his hands on power is a risk we can not afford to take".
The Labour Party may also attempt to force a general election or seek to form a minority government.
"I believe Jeremy Corbyn getting his hands on power is a risk we can not afford to take", she added.
Pressure is mounting on May to delay the vote and ask for more concessions from the European Union at a Brussels summit at the end of next week.
May could return to Brussels seeking changes to the Brexit deal and bring it back to Parliament for another vote.
Barclay said Britain would enter "uncharted waters" if it loses the vote, but May could stay on as prime minister.
Serena Williams' surprising advice for best friend Meghan Markle
It's a total style switch-up for the duchess, who usually wears dresses or fitted trousers . " She will be an unbelievable mom. Over the summer, Markle wore a white pair of flowy trousers to Wimbledon, where she sat next to Middleton.
Meanwhile Defence Minister Tobias Ellwood said he would back the deal - but indicated that unless it was passed quickly he might support a second referendum because the original decision to Leave may "no longer represent a reflection of current intent".
During the meeting, which was called by May, Chief Whip Julian Smith said the government is heading for a defeat, while Amber Rudd, the work and pensions secretary, became frustrated and asked "What do you want to do, prime minister?" according to a report in the Daily Telegraph.
That means it is part of the single market.
May has been battling her own party on Brexit ever since she lost her majority in the snap election of June 2017 and has somehow survived, with her plans inching forward.
"My undertsanding is that we will have a vote on Tuesday and we are looking to win that vote", Kwarteng told Sky News.
"They might decide to retire or they might decide to abandon the party whip, that has happened before".
Graham Brady, the influential chairman of the 1922 Committee of Tory lawmakers, publicly suggested May should postpone Tuesday's vote to give her time to strike a compromise with pro-Brexit lawmakers over a mechanism for ending the so-called Northern Ireland backstop. "We have got a good shot of winning". "There's still two full days of debate". However, it needs to be approved by Parliament - with MPs due to vote on Tuesday.
Labour is considering its options if Mrs May is defeated and would hold talks with other opposition parties about how to proceed.