"We gave them the choice, they voted to leave the European Union and it is up to us to deliver".
The Times newspaper reported that senior ministers were urging May to delay it for fear of a rout.
But the source said the Prime Minisiter has fiercely opposed any such vote. Only this morning, Andrea Leadsom, Leader of the House of Commons, told the Radio 4 Today programme that it was a "very important breach" of centuries of convention of legal privilege to publish legal advice in this way.
The day before the vote, on December 10, the EU's top court will deliver a judgment on whether Britain can unilaterally halt Brexit.
"The agreement that is on the table - the withdrawal agreement and the agreement on the future relationship - are, in our view, the only and best possible to organise an orderly withdrawal", he said.
The vote, passed by 311 votes to 293, is the first time in history Parliament has held a Government in contempt. He said: 'The idea there's an option of renegotiating at the 11th hour is simply a delusion.
"The alternative is uncertainty and risk - the risk Brexit could be stopped, the risk we could crash out with no deal". "Either will leave us a fractured society and divided nation".
She suggested MPs could be "given a role" in deciding whether to activate the backstop, which is created to stop the return of a physical border.
The legal advice document prepared by United Kingdom attorney-general Geoffrey Cox, at the heart of the rare contempt motion against the government in Parliament earlier this week, warns the terms of the Irish backstop could trap the United Kingdom in "protracted and repeated rounds of negotiations" with the European Union in the years ahead.
The government has published the full legal advice it was given on Theresa May's Brexit plan after MPs found the government to be in contempt of parliament for refusing to do so.
May has repeatedly promised there would be no trade border between Northern Ireland and Great Britain. "Do we extend what I call the implementation period?"
She said: "I am talking to colleagues about how we can look at parliament having a role in going into that and coming out of that".
"Overwhelmingly, the message I've heard is that people want us to get on with it". A source told BuzzFeed News Mrs May's chief of staff Gavin Barwell and chief whip Julian Smith have spoken about the prospect of a second public vote on Brexit. But lawmakers who attended the meeting said he did not offer a solution to persuade them to back it.
Shadow Brexit secretary Sir Keir Starmer said that the 33-paragraph document revealed "the central weaknesses in the Government's deal". Another said it was: "Too little, too late".
And he said that - despite assurances from both London and Brussels that it is meant to be temporary - the protocol would "endure indefinitely" under global law until another agreement takes its place.