Her comments came as critics said Mrs May could be forced to stand down if her deal was defeated.
Ms Rudd told The Times that, should the deal be voted down, she would prefer a so-called Norway-plus model for Brexit that would involve staying part of the European Economic Area.
Amber Rudd has suggested that a Norway-plus deal could provide an alternative to Theresa May's Brexit proposals if they are rejected in Parliament.
The figures have been released as Mrs May desperately seeks to get parliamentary and public approval for her Brexit deal, amid fears her government could collapse if not.
Labour MPs Naz Shah, Imran Hussain, Judith Cummins, John Grogan and Alex Sobel were joined by Tory Philip Davies in opposing the deal negotiated with the EU.
However, North Down independent unionist MP Lady Sylvia Hermon is expected to back the prime minister.
Ms Rudd became the first cabinet minister to publicly discuss a "Plan B" if Mrs May's deal was rejected.
One Tory MP said: "The DUP want her head on a plate".
The DUP has spoken out about the proposed deal, saying they can't support it in its current form.
"Bradford is one of the most deprived cities in the United Kingdom, with high unemployment and low wage growth, and this deal will do nothing to improve this situation, but will instead leave people even poorer".
"It guarantees that even in the unlikely event that the UK's future relationship with the European Union is not in place by the end of the implementation period in December 2020, there will be no hard border between Northern Ireland and Ireland".
Being in the EEA after Brexit would keep the United Kingdom in the single market, meaning goods, services and people could continue to move within the bloc in the same way as before, therefore limiting the potential disruption to the economy.
"They see her as duplicitous", one Conservative MP said, adding that they believed events next week could lead to a snap general election.
"The outcome of that is that she'll have to come back to parliament again and hopefully this time with a deal we will accept".
"I will certainly not be voting to hand over £39bn to the European Union with nothing in return in a deal which keeps us shackled to the European Union in perpetuity".
Mr Dodds says if ratified the deal would be an global legally-binding treaty, which would place a customs and regulatory border between Northern Ireland and Great Britain contrary to previous pledges from Prime Minister Theresa May.
"It will mean years ahead of wrangling which will not be good for business or jobs".
If the Government passes the deal the legalisation will be introduced.
"It would be much better to have firm arrangements in place now".
In a joint foreword, Labour former foreign secretary David Miliband and Tory ex-minister Jo Johnson - who quit his Government role in November over Brexit - said: 'Norway-plus would represent a long-term commitment to pay to benefit from the European Union's regulatory structures while choosing to be outside it'. "I will not vote for the Prime Minister's blank cheque and I will oppose a no deal Brexit with every fibre of my being".
Mr Davis said: "I don't think [Mrs May] win". I say this as this is purely a stepping stone to get to another place. "The men think they are standing on principles but they're not getting things done".
"It is for these reasons that I will be voting to back the deal and will back the Prime Minister".
Since October previous year , Nissan has recalled more than 1 million vehicles in Japan because of improper inspections. It was reported that several employees admitted to the regulators that they had not been following protocol in tests.
Import growth was 3 per cent, the slowest since October 2016, and a fraction of the 14.5 per cent seen in the poll. The customs data showed that annual growth for exports to all of China's major partners slowed significantly.
An global team of researchers has reportedly hit a new gene breakthrough that may lead to the development of anti-obesity pills. However, the estimated number of dieters may be decreasing due to the acceptance of obesity and the body positivity movement.
Treating them with chemotherapy and hormone therapy after surgery doesn't improve outcomes more than hormone therapy alone. Ethnically, 79 percent were non-Hispanic, 9 percent were Hispanic and 12 percent were of unknown ethnicity.
Trump and Kelly have privately argued at times and complained about each other to confidants, sometimes in colorful language. He announced Friday that he'll nominate William Barr, who served as attorney general under President George H.W.
The Blitzboks made amends for their defensive failings when they sacked a Kiwi ball-carrier behind the tryline after half-time. New Zealand have staved off the threat of a first-ever exit in the pool stages of a World Series sevens men's tournament.
The impasse is on vivid display in Hodeida, a Red Sea port city where Yemen imports 70 percent of its food and humanitarian aid. Saudi-led airstrikes against the rebels are compounding the misery - wiping out entire neighborhoods and destroying hospitals.
Robertson told the Los Angeles Times in 2007 that he struggled with a crack cocaine addiction during his previous year in the NFL. The impact sent Robertson's auto into oncoming traffic, where it was struck again by a 2018 Hyundai Sonata.
Kevin Hart steps down as Oscars host
F*** 'em if they can't take a joke! Approximately 48 hours later, Hart stepped down from the prestigious post. Hart initially failed to issue an apology, insisting he had addressed the situation "several times" already.
Iran: US sanctions are 'economic terrorism'
Rouhani drew parallels with the sanctions and other pressure faced by the countries attending the conference. The "illegal U.S. sanctions" are " a form of economic terrorism ", Rouhani said, as cited by Iranian media.
Prince Harry at Neo-Nazi Group's Target: 3 arrested
Mr Koczorowski came to the door of his London home wearing a hooded top emblazoned with the Atomwaffen Division logo. It's believed there are 10 to 15 members of the group in the United Kingdom and some European countries.
IPhone Sales Fail Triggered "Fire Drill" at Apple
Before we talk about what made iPhone XR bag the coveted spot, let us give you a quick recap of the phone's camera specifications. The video stabilization system is also among the best that have been tested, ensuring smooth video playback with little shakes.
There's a bacon vending machine at Ohio State University
The Ohio Pork Council sponsored the machine, and it received bacon donations from Smithfield, Hormel and Sugardale. It says it's a fun way to help the meat science program at the school and a good way to promote the pork industry.