Officially slated for the week of January 14, the Commons vote is widely expected to be held on January 15.
But parliamentary opposition to her deal remains fierce, with the main sticking point being the safety net "backstop" measure - which would guarantee no hard border is erected on the island of Ireland in the event that post-Brexit trade negotiations between the United Kingdom and the bloc prove unsuccessful.
She repeatedly sidestepped questions about whether she would keep putting the deal back to MPs if it gets rejected, instead saying: "If the deal is not voted on, this vote that is coming up, then actually we are going to be in uncharted territory".
But Brexit minister Kwasi Kwarteng dismissed suggestions that the government had accepted it would lose next week's vote and was planning on returning to Brussels.
On the other side of the Tory divide, pro-EU veteran Ken Clarke said May's deal - which he would be prepared to support - is "dying", and he would be "amazed" if the mood of MPs had changed over the Christmas break. "So far, nobody has put forward an alternative on all those issues", she said.
But a former Thatcher cabinet minister, John Redwood, said a no-deal Brexit "will work just fine" despite the "idiotic" warnings about potential shortages of food and medicines.
He added: "The priority now is to await events, monitor what is happening (with) the ratification procedure on the United Kingdom side and no, there will not be any meeting between the Commission and our negotiator teams".
Meanwhile, more than 200 MPs have signed a letter to Theresa May, urging her to rule out a no-deal Brexit.
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In an attempt to prevent the United Kingdom falling out of the European Union without a deal, more than 200 lawmakers have signed a letter to May urging her to rule out a no deal.
The MPs have been invited to meet the prime minister on Tuesday.
The meeting is one of a series being organised by Mrs May, who is also hosting drinks receptions for Tory MPs on Monday and Wednesday as part of an charm offensive to win support for the Brexit deal.
"Don't let the search for the ideal [Brexit] become the enemy of good", May told the BBC's Andrew Marr Show.
He added: "In terms of precisely what is required, that is a judgement for the whips and for the house, but we are committed to ensuring the legislation is in place".
Brexit related bills now before Parliament - the Trade Bill, the Agriculture Bill, the Healthcare Bill, the Fisheries Bill, the Immigration Bill and the Financial Services Bill.
"What colleagues have said they want me to do is to deliver Brexit, which is what I am working on doing and also deliver on the agenda I set out when I first became Prime Minister".
However, according to May's former Foreign Minister and clean exit proponent, Boris Johnson, the PM's crusade to pass her "lamentable" Brexit deal and the government's "grim" warnings against opposition won't work. I think the situation - as it always does - has developed, it evolves. "We don't know what the numbers are", he told BBC.