Theresa May has said the Commons vote on her Brexit deal will "definitely" go ahead next week as she vowed to redouble her efforts to win MPs round.
She said she would set out new measures on Northern Ireland and look at giving MPs more say in shaping negotiations over future trade relations.
Warning of "uncharted" territory if MPs rejected the deal, she declined to rule out holding more than one vote.
But one Tory Brexiteer said support for a no-deal exit was "hardening".
And a poll carried out for the People's Vote campaign suggests fewer than one in four voters support the prime minister's Brexit deal.
The UK is due to leave the EU on 29 March 2019.
A deal on the terms of the UK's divorce and the framework of future relations has been agreed between the prime minister and the EU - but it needs to pass a vote by MPs in Parliament before it is accepted.
MPs are expected to be asked to vote on it either the 14 or 15 of January.
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The crunch vote was due to take place in December but was postponed at the last minute as Mrs May faced almost certain defeat amid opposition from many of her MPs, as well as Labour and other parties.
Asked by the BBC's Andrew Marr if the vote would "definitely" go ahead in the second week of January, she replied "yes, we are going to hold the vote".
She said she truly believed hers was a "good deal" for the country and that it was up to its opponents to spell out the alternatives to it.
Asked what had changed since last month, she said the EU had agreed to some "changes" and she was continuing to talk to European leaders as she tried and give MPs the "confidence" to support the deal.
She promised to give more detail in three areas in the coming days:
- Specific measures for Northern Ireland
- A greater role for Parliament in negotiations on the next stage of future UK-EU relations
- Further assurances from the EU to address concerns over the Irish backstop
She said there were a "number of ways" of giving MPs more input in the next phase of the Brexit process, including allowing them a real say in shaping the "mandate for the negotiations for the future relationship".
"The deal is on the table. We've got people who want to see their perfect Brexit. And I would say don't let the search for the perfect be the enemy of the good. The danger there is that we end up with no Brexit at all."
Asked whether she was prepared to stand down as PM and let someone else take over talks over the future relations, Mrs May - who survived a vote of no confidence last month - said the party had made it clear they wanted her to "deliver on Brexit and that is what I am working on doing".
Public polled on Brexit
Meanwhile, a poll of more than 25,000 Britons suggests Labour would be punished by voters if the party either ends up backing the government's deal or does not actively oppose it.
The YouGov poll, carried out for the People's Vote campaign which is demanding another referendum, suggests 75% of Labour supporters would prefer a final say on Brexit.
Jeremy Corbyn has previously said the decision to leave the EU cannot be reversed.
Shadow health secretary Jonathan Ashworth told Andrew Marr that it was completely wrong to suggest, as some have done, that Labour was "enabling Brexit".
"We are committed to voting against Theresa May's deal. It wouldn't surprise me if it was delayed, that shows how beleaguered this Tory cabinet is.
"But then if that is voted down, it is incumbent upon the government to come forward with alternative proposals and try to renegotiate."
The poll also suggested:
- 22% of all Britons back Mrs May's deal, rising to 28% among Leave voters
- 53% of Britons believe they - instead of MPs - should be given the final say on Brexit, once those who responded "don't know" were removed
- And among those who said they would vote in another referendum, the survey suggested 54% would back remaining in the EU, compared to 46% for Leave
Some Conservative MPs continue to believe the deal does not represent the Brexit the country voted for in 2016 - with some happy for the UK to leave the EU with no deal.
"If there has been a change it is a hardening of attitudes among MPs to a no deal," Peter Bone told the Sophy Ridge show on Sky News.
He said there was increasing evidence that a no deal was "absolutely OK".
The best way to "get on" with Brexit was to leave without a deal, he added: "There was no question I remember in the referendum about a deal or not. It was leave or remain. The way you leave is to come out on March 29."
Mrs May has spoken a number of EU leaders in recent days about the controversial Irish border "backstop", which is designed to prevent physical customs checks on the island of Ireland.
The Democratic Unionist Party - whose support the Conservative Party relies on for a majority in the House of Commons - wants to make sure the backstop is temporary and that the UK, including Northern Ireland, can exit from it without EU approval.
Earlier this week, a leading figure in the party said there is "no way" it would back the deal.
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