May has a week to find a compromise on the conflicting Brexit demands from the north and south of Ireland, just as a political scandal threatening the Irish government could further undermine her chances of success.
It comes amid growing concerns in Europe that the impasse over the Border question is unresolved because of the uncompromising position of the DUP, which is propping up the Tory government.
The pro-Brexit Democratic Unionist Party (DUP), which strongly supports British rule in Northern Ireland, has said it will not countenance the province operating under different regulations to the rest of the UK.
However, if May insists on leaving the EU customs union, there will have to be a "hard" border - and if there is, says Ireland's Prime Minister Leo Varadkar, he will veto any negotiations between the EU and the United Kingdom on a free trade deal after it leaves the Union.
European Union officials and diplomats have in recent weeks been scoping out terms for a transition and various kinds of free trade agreements - work meant to speed up the start of talks on those issues in anticipation of agreement to open the second phase of Brexit negotiations at the December summit. Customs rules to be decided as part of the future trade talks.
However, the Irish government is looking for firmer commitments.
Enterprise Ireland’s Construction Adviser John Hunt
The progress is being made ahead of a crunch meeting between Theresa May and EU Commission President Jean-Claude Juncker over lunch on Monday.
Channel 4 has posted a video on their Twitter page to see how British people were reacting to the Northern Ireland border issue.
It is seeking to offer more vaguely-worded commitments and guarantees to Ireland around the issues, so that it will be able to move onto trade following a crucial European Union summit on 15 December.
An EU negotiator told the Times: 'After sufficient progress on withdrawal we will open the next two phases of negotiations, first of all on a transition period and then on the future partnership.
The precise timing of a formal offer of a transition, which European Union officials have long said will essentially mean Britain staying in all European Union programmes but without a vote, is unclear but could come as early as January, officials have said - though it would only be binding once the divorce deal is signed and ratified by both parliaments, probably in early 2019.
A UK Government source added: 'In return for making progress on the withdrawal agreement the European Union will move on transition by the end of January with a fair wind, ' they said. It's a bit petty, isn't it, really?
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