The Democratic Unionist Party has had further talks in Downing Street, as the future of Boris Johnson’s Brexit deal hangs in the balance.
The PM is in a race against time to get a deal before Thursday’s EU summit, as discussions continue in Brussels.
Differences remain on proposed customs and tax arrangements, and how to get support for them in Northern Ireland.
But the PM must persuade the DUP and Brexiteer Tories to back any deal with the EU to get it through Parliament.
The issue of the Irish border – and how to handle the flow of goods and people across it once it becomes the border between the UK and the EU after Brexit – has long been a sticking point in the negotiations.
The border is also a matter of great political, security and diplomatic sensitivity in Ireland.
The backstop – the solution to border issues agreed by Theresa May – proved unpalatable to many MPs so Mr Johnson has come up with new proposals to dispense with it.
However, they would see Northern Ireland treated differently from the rest of the UK – something the DUP, among others, has great concerns about.
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The BBC’s Brussels reporter, Adam Fleming, says there has been a shift in emphasis in the Brussels talks away from issues around customs towards matters surrounding the so-called consent mechanism – the idea the prime minister came up with to give communities in Northern Ireland a regular say over whatever comes into effect.
The DUP is understood to be most concerned about this issue too. The party also fears the creation of a “customs border” in the Irish Sea, which would require checks on goods between the rest of the UK and Northern Ireland.
The UK is due to leave the EU at 23:00 GMT on 31 October and Mr Johnson has repeatedly insisted this will happen, regardless of whether there is a deal or not.
The EU’s chief negotiator, Michel Barnier, will update the bloc on the state of the negotiations later when he briefs commissioners and ambassadors.
Mr Johnson, who spoke to his Irish counterpart Leo Varadkar on Wednesday morning, is also expected to update the cabinet.
Meanwhile, one senior EU diplomat has told journalists in Brussels it is now too late for EU leaders to formally approve a revised Brexit deal at the summit.
They said the most they could do was give a provisional thumbs-up – “a political yes” – to whatever emerges from the talks pending the release of the final legal text.
The BBC’s assistant political editor Norman Smith said there were suggestions the talks had gone as far as they could “unless and until” the PM could bring the Democratic Unionists on board.
The DUP are due to issue a statement later, following their latest round of talks in Downing Street.
After a 90-minute meeting on Tuesday, they said “it would be fair to indicate gaps remain and further work is required”.
The party’s Brexit spokesman, Sammy Wilson, said any customs agreement must be subject to the consent of unionists and nationalists before it comes into force under the terms of the 1998 Good Friday Agreement, which established Belfast’s power-sharing arrangements.