Theresa May has told MPs she will seek to re-open negotiations with the EU over the Northern Ireland backstop.
The PM said she would go back to Brussels to get a "significant and legally binding change" to the controversial proposal, which aims to stop the return of border checks.
The EU has said it will not change the legal text agreed with the UK PM.
Mrs May said she knew there was a "limited appetite" in the EU, but she believed she could "secure" it.
She is expected to have phone calls with key EU leaders throughout the day ahead of a series of Commons votes over the future direction of Brexit, and has already spoken to the President of the European Commission Jean-Claude Juncker and the Irish Taoiseach (Prime Minister) Leo Varadkar.
Mrs May said the vote later would be a chance to "send a clear message" to EU on the backstop.
MPs are now debating what the next steps could be for the #Brexit deal. Our Clerk of Legislation, Liam Laurence Smyth, explains more.— UK House of Commons (@HouseofCommons) January 29, 2019
Watch: https://t.co/ARzfvLxhAw #BrexitNextSteps pic.twitter.com/ONKTgVfFnN
But the EU was "standing tough" on its position of no renegotiation and they were "mesmerised" with what was happening in Parliament, BBC Europe editor Katya Adler said.
Senior Brexiteer rebels - who voted down the PM's deal last month - have indicated they would be willing to back the rest of the UK-EU Brexit deal if she gets legal changes to the backstop.
The backstop is the insurance policy in Mrs May's plan to prevent checks on goods and people returning to the Northern Ireland border, which some MPs fear could leave the UK tied to the EU's rules indefinitely.
But some MPs from the PM's own backbenches, who backed Remain in the referendum, will support rival proposals to try and rule out the UK leaving the EU without a deal.
Labour leader Jeremy Corbyn said Mrs May herself was the "obstacle to a solution" and that, whatever happened in the votes later, it had "now become inevitable" that the government would have to extend Article 50 - the mechanism which means the UK leaves the EU on 29 March.
MPs put forward a string of amendments to modify the prime minister's Brexit plan after it was voted down by an historic margin on 15 January.
Speaker of the House, John Bercow, has named seven amendments to be debated and voted on, including one from senior Tory MP Sir Graham Brady calling on "alternative arrangements" to the backstop, and one from Labour MP Yvette Cooper, which could delay the exit date by up to nine months.
Opening the debate, Mrs May said: "This House has left no-one in any doubt about what it does not want. Today we need to send an emphatic message about what we do want."
A series of votes on the amendments is expected from 19:00 GMT (8am NZT).
Conservative MPs have been instructed by the government to vote for Sir Graham's amendment, which could pave the way for a plan known as the "Malthouse Compromise".
Engineered by both Leavers and Remainers, the proposal includes extending the transition period for a year and protecting EU citizens' rights, instead of using the backstop.
The prime minister's spokesman said Mrs May would "engage" with her colleagues to discuss the plan, but she would also be looking at a possible time limit or a unilateral exit clause to the backstop as other "alternatives".
But what will come first is the vote in the Commons, and Mrs May appealed for the backing of the "Brady" amendment as the next step, saying it would "give the mandate I need to negotiate with Brussels an arrangement that commands a majority in this House - not a further exchange of letters, but a significant and legally binding change to the withdrawal agreement".
She added: "The time has come for words to be matched by deeds. If you want to tell Brussels what this House will accept, you have to vote for it. If you want to leave with a deal, you have to vote for it. If you want Brexit, you have to vote for Brexit."
Nigel Dodds, the Westminster leader of the Democratic Unionist Party (DUP) - whose MPs Mrs May's government relies on to win key votes - welcomed the announcement, saying: "From day one ... we rejected the backstop and argued for legally binding change within the withdrawal agreement. The decision to seek the reopening of the text is a sensible step forward by the prime minister."
The Labour Party and a number of Remain-backing MPs are supporting Ms Cooper's amendment that would create a bill enabling Article 50 to be delayed by up to nine months if the government does not have a plan agreed in Parliament by the end of February.
Labour said it was supporting the amendment because the bill it would create could "give MPs a temporary window to agree a deal that can bring the country together".
However, Mr Corbyn, told the Commons they wanted a shorter window of three months to allow time for a deal to be finalised.
"The Labour Party will back the amendment tonight because to crash out without a deal would be deeply damaging for industry and economy," he said.
He added: "It's quite clear to me that the first duty [MPs] have is to block a disastrous no deal and I hope amendments to that effect will indeed be carried by the House later."