The prime minister did not discuss resigning after her latest defeat because a government led by her had recently won a confidence vote in the commons, the PM's spokesman said.
The deal was defeated in the Commons on Tuesday evening by 149 votes.
Theresa May has been described as a "rabbit in the headlights", too frightened of Brexiteers in her party to really say how bad no-deal would be for country, according to a Labour MP.
Hours before tonight's vote, ministers announced worrying new tariffs that are likely to provoke more accusations of scaremongering after months of apocalyptic warnings about the impact of a no deal Brexit. But what I hope is a cause for optimism is that the Prime Minister seemed to discuss what many of us have been waiting for, for a long time, the opportunity for Parliament to give direction either in terms of a different kind of deal or, indeed, she even mentioned a second referendum.
"MPs now need to rule out no deal as soon as possible and, after two-and-a-half years of failed negotiations, making Britain a laughing stock, it is time for a public vote".
"I am passionate about delivering the result of the referendum, but I equally passionately believe that the best way to do that is to leave in an orderly way with a deal and I still believe there is a majority in the House for that course of action", May said.
Mrs May declined to do so, sticking by her deal as the best way to Brexit, but added money had been made available for no-deal preparations.
Some of her colleagues around the Cabinet table think it shows she has to tack to a closer deal with the EU.
Channel 4 News host Krishnan Guru-Murthy said: "Theresa May has lost her voice - this is very bad".
She said she was "not frightened" of the people in her Birmingham Yardley constituency who voted to leave, saying if they do not like her views they can vote her out.
"I feel like MPs like myself who want to honour the referendum have been put in a bind".
Tory Brexiteer Peter Bone (Wellingborough) asked Mrs May to back the Malthouse amendment, which aims for the United Kingdom to leave the European Union without a deal but also secure a transition period until the end of December 2021.
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