Channel 4's "Real Brexit Debate" was aired after rival plans by the BBC and ITV for a televised showdown involving Mrs May and Labour leader Jeremy Corbyn fell through.
Kicking off Sunday night's debate, the woman said: “Leavers reject Theresa May’s deal and her treasonous behaviour. She is ceding control, not taking back control.
“And how dare she abandon the rights of the citizens of Northern Ireland?”
Responding to that host Krishnan Guru-Murthy said: “Well treasonous is very strong language”.
It comes after a protestor carried a noose and called for the Prime Minister to be hanged at a Brexit protest led by far-right thug Tommy Robinson in Parliament Square today.
Tory deputy chairman James Cleverly made the plea in support of Mrs May's deal, arguing it delivered on what people voted for.
He said: "Our deal delivers on what people voted for. It takes back control of our money, our borders, our laws.
“It means we can get on with Brexit and give more time to focus on other important issues like the NHS."
He added: "The only thing we know for sure is that rejecting this deal means damaging uncertainty and, as a Brexiteer, the thing that worries me the most is the risk we do not leave the EU at all."
In his concluding remarks he urged Brexiteers to "take the deal and get out" of the European Union ahead of Tuesday's crunch Commons vote.
But arch-Brexiteer Jacob Rees-Mogg said the deal "does not do what the Prime Minister said" on the customs union, the jurisdiction of the European Court of Justice and a border between Great Britain and Northern Ireland.
He added: "This is all about trust. Across Europe politicians are distrusted – there are riots in France and troubles in Italy.
"Everybody agreed to accept the result of the referendum. Now Theresa May has said one thing and come back with a deal that does another."
Shadow international trade secretary Barry Gardiner claimed the Prime Minister’s deal would “rip the country in half”, saying it satisfied nobody.
He said Labour "would negotiate a permanent customs union and a strong single market deal that protects workers' rights and environmental standards".
He said he “didn’t understand” the People’s Vote position – despite it being one of Labour’s official “options”.
Caroline Lucas, co-leader of the Green Party, who was widely credited with winning the debate on social media, said Mrs May was asking the British people to go for a “blindfold Brexit”.
She said: “Brexit is a project for the right, by the right and why Labour would support it I just don't understand".
She went on: “One thing that is already clear by tonight is that this decision cannot be left to the politicians. We simply can’t agree.
“This not a parlour game or debating society. These are real people with real lives.
“That’s why the people need to have their say. A people’s vote would be your first chance to vote upon the facts.
“Don’t leave it to the Westminster elite to decide for you”.
Resposding to her, Mr Rees-Mogg called it a "losers' vote" and asked: "If you get a second vote and lose that, how long will it be before you ask for the third?"
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