The Work and Pensions Secretary became the first Cabinet minister to publicly discuss the merits of a “Plan B” if May crashes to defeat in Tuesday’s crunch Commons vote.
She also suggested a second referendum was another potential outcome that might be sought by MPs if the deal is thrown out.
The former home secretary said the alternative “seems plausible not just in terms of the country but in terms of where the MPs are,” but conceded that “nobody knows if it can be done”.
Rudd predicted a “chaotic” period if the Government is defeated.
“If it doesn’t get through, anything could happen – People’s Vote, Norway-plus, any of these options could come forward and none of them are as good as the current arrangement we have got with the Withdrawal Agreement to vote on on Tuesday.”
Her comments could be viewed as an attempt to win over Brexiteers who might prefer May’s deal, even with its controversial Northern Irish backstop, to a Norway-plus future inside both the single market and customs union or the possibility of another referendum reversing the 2016 vote.
“What we need is a compromise deal, that’s what the Prime Minister has proposed and I would urge my colleagues to think about, first of all, why people voted to leave the European Union, what their interpretation is of that; and secondly, what the alternatives are.
“This is why I think it is important for people not just to think why they don’t particularly like the Withdrawal Agreement but what they would like better that is available and would get through the House of Commons.”
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.
Eurosceptic former party leader Iain Duncan Smith cautioned against the PM and her Cabinet deciding to “brazen it out”, saying such an approach would be a “disaster”.
“How the PM responds after the vote matters more than anything else she has done,” he told the Daily Telegraph.
“I believe that if the response is, ‘we’ve lost but we will do this all over again’, it will become a leadership issue.”