“And am I going to see this through? Yes,” she said.
However her opponents within the Tory party, led by the arch Brexiteer Jacob Rees-Mogg, had already launched a campaign to force her out through a vote of no confidence.
The pound fell against the dollar and euro and stocks in banks and housebuilders slumped as it appeared Mrs May could not get her Brexit plan through Westminster, shortening the odds on No Deal .
At a press conference in Number 10, Mrs May said: “I believe with every fibre of my being that the course I have set out is the right one for our country and all our people.
“Leadership is about taking the right decisions, not the easy ones.
“My job is to bring back a deal that delivers on the vote of the British people… ending free movement … ensuring we are not sending vast annual sums to the EU any longer, ending the jurisdiction of the European Court of Justice, but also protects jobs and protects people’s livelihoods, protects our security, protects the Union.
“I believe this is a deal which does deliver that, which is in the national interest. Am I going to see this through? Yes.”
Mrs May’s fate now appears to rest with her Leave-supporting Environment Secretary Michael Gove, who has so far remained in the cabinet.
He rejected an offer to become her third Brexit Secretary in 18 months following Dominic Raab’s resignation yesterday.
Mrs May refused his pre-condition of rewriting her 585-page draft withdrawal agreement and delaying a sign-off meeting of EU leaders scheduled for November 25.
If Mr Gove quits, the loss of confidence in Mrs May would almost certainly be irreparable.
In an extraordinarily fast-moving day at Westminster, Mrs May suffered five resignations before addressing MPs on her draft agreement at 1030am.
Mr Raab and his fellow Brexiter Pensions Secretary Esther McVey walked out of the cabinet, saying the plan, which Mrs May had touted as a breakthrough in Downing Street barely 12 hours earlier, threatened the Union and British democracy.
Also leaving the government were Northern Ireland minister Shailesh Vara, Brexit minister Suella Braverman, and education parliamentary private secretary Anne-Marie Trevelyan.
Ms Braverman said generations of people would see plan “as betrayal”.
After Mrs May insisted in the Commons that her plan was in the national interest, she was assailed by critics in her own party who told her MPs would never agree to it.
One told her she ought to resign, while another pleaded with her to “face reality.”
He told party members last night that if the crisis did not lead to a general election, he would support “all options remaining on the table”, including a second EU referendum.
Mrs May’s previous allies in the DUP, on whom she has relied for a majority, also rejected the deal, accusing her of breaking promises and not listening to criticism.