Raab announced his resignation on Thursday morning with Work and Pensions Secretary Esther McVey following suit later in the morning.
Nobody had produced an alternative proposal that would deliver on the referendum and ensure no "hard" border in Ireland, she said.
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She was greeted by mocking laughter when she said her plan would provide for a "smooth, orderly" Brexit. Corbyn demanded that the government should withdraw the deal.
"You deserve a Brexit secretary who can make the case for the deal you are pursuing with conviction".
Raab, whose resignation was the most significant, said: "I can not reconcile the terms of the proposed deal with the promises we made to the country in our manifesto at the last election".
During her Downing Street statement, she also pushed that the deal gave back "full control of our money", she said, "so we decide ourselves how to spend it on priorities like our NHS".
The plan has also failed to find favour among Tory voters, the survey suggests, with 41% of 2017 Conservative voters opposing it, against 28% backing the Prime Minister.
On Thursday morning, Barnier is expected to announce an European Union summit on the Brexit issue with the United Kingdom expected to leave on 29 March.
Labour said the Government was "falling apart before our eyes" and the pound dropped sharply after Mr Raab's resignation.
The massive resignations came as May was giving a fighting statement in the parliament in a bid to rally support to her deal.Her series of public remarks were meant to send a message: The draft deal on the table is the only best choice for Britain to leave the trading bloc, and she is the most suitable leader to deliver the Brexit as mandated by the 2016 referendum. "No democratic nation has ever signed up to be bound by such an extensive regime, imposed externally without any democratic control over the laws to be applied, nor the ability to exit the arrangement", he said.
Trump Goes Ballistic On Mueller: 'Absolutely Nuts'
He wasn't close to done: "These are Angry People, including the highly conflicted Bob Mueller, who worked for Obama for 8 years. He tweeted on Thursday that investigators were "threatening" people to provide "the answers they want".
Looking exhausted and drawn, she said she believed in her Brexit plan "with every fibre of my being", and ruled out a People's Vote.
'Here is my letter to the PM explaining my reasons, and my enduring respect for her'.
The deal would then return in early December to the UK Parliament, where May faces a tough battle to win the approval of MPs.
Rees-Moog told the press that Boris Johnson or former Brexit secretary David Davis - both of whom already resigned from the government earlier this year - would be better choices as prime minister.
She could withdraw the current deal and ask the European Union for an extension of negotiations, but that would likely be fatal for the already embattled prime minister. More resignations have followed. Sterling dropped 1.1% to 1.28 U.S. dollars and was 1.2% lower at 1.13 euros.
It was always going to be a challenge, but it's hard to imagine how Prime Minister Theresa May can recover from the biggest blow so far: the resignation of Dominic Raab, her chief negotiator and the minister responsible for Brexit.
Rodney Atkinson: I am sure one of the arguments against the Prime Minister's deal is in Cabinet was that 'okay, whether we agree with it or not, we know that Parliament will not agree to it.
We can choose to leave with no deal, or risk no Brexit at all.
She said if MPs rejected it they faced Britain leaving without agreement, which experts says could lead to potentially catastrophic economic and legal disruption.
Ms Soubry added: "No PM deserves to be so badly treated".
Sputnik: It looks to me that the country would be better off to actually have a general election and have totally new players to actually get us out of this mess. "The people of the United Kingdom deserve better".
The deal also includes protections for European Union citizens living in Britain and a transition period lasting until at least 2020, during which time future trade agreements could be negotiated.
Welcoming the UK Cabinet's collective agreement to accept the withdrawal document, Mr Tusk said: "Of course, I do not share the Prime Minister's enthusiasm about Brexit as such".