A new BBC survey has shown that just over 42% of Northern Irish citizens want a united Ireland. But it also risks causing more domestic trouble for May, who needs to keep her divided Cabinet together and the Northern Irish party that props up her government onside.
The customs paper published by the British government earlier this week would see Britain effectively agree to apply European Union customs tariffs in order to avoid the need for checks at the border between Northern Ireland and the Republic, according to British media.
The comments followed speculation at Westminster that Mr Davis had considered quitting over a dispute regarding backstop proposals on how to deal with the issue of the Northern Ireland border if a preferred withdrawal trade deal is not sorted out with the EU.
In a bid to calm Brexiteers, the Prime Minister held one-on-one talks with Mr Davis, Boris Johnson and Liam Fox on Thursday morning ahead of a meeting of the Brexit "war cabinet" at lunchtime.
Instead it would see Britain staying tied to the EU's customs union for up to another year after an nearly two-year transition period if there were any delay in implementing a Brexit deal.
Noble and Adrian send messages to West Ham teammate Manuel Lanzini
All eyes will now be on Argentina coach Jorge Sampaoli to see who will be replacing Lanzini in the squad. Lanzini made 29 appearances for West Ham last season, scoring five goals and creating nine assists.
He questioned whether a temporary backstop could "secure the absence of a hard border in all circumstances" and said it might mean businesses and public authorities having to cope with several changes.
These figures produced a total cost for UK-EU trade in goods of about £17bn-£20bn a year, he said.
Another paragraph clearly states the temporary customs arrangement will be "time-limited" and will come into force after the Brexit transition period ends in December 2020.
Minister Theresa May unveiled a one-year "backstop plan" for the Irish border on Thursday. Amendments passed by the House of Lords, and due for an MPs' vote next Tuesday, would require the Government to try to negotiate a customs union and continued membership - alongside non-EU countries like Norway - of the European Economic Area (EEA).
That sounded "paradoxical", Barnier said, reflecting "some kind of nostalgia" for European Union membership among British ministers who wanted to keep the benefits without following the regulations. The Irish Republic is primarily interested in avoiding a hard border and is likely to accept the compromise, as Irish Foreign Minister Simon Coveney underscores that it is "vital" that a legally-binding backstop agreement is in place.
And Labour MP Ian Murray, a supporter of the People's Vote campaign for a second referendum, said: "Theresa May's flimsy Brexit proposal has lasted less than 24 hours".