Mrs May chaired a meeting of the inner Cabinet on Brexit progress Mrs May set out in June proposals for a "temporary customs arrangement" to ensure that the border between Northern Ireland and the Republic remains open in the case that no broader EU/UK trade agreement has been finalised.
"Trade from Great Britain into Northern Ireland would be in danger of restriction".
"I am sure the Prime Minister is well aware of the grave responsibility which lies on her shoulders".
A Downing Street spokeswoman emphasised Friday that this would be "temporary", saying: "The prime minster would never agree to a deal which could trap the United Kingdom in a backstop permanently".
Mr Coveney also suggested the entire debate over Prime Minister Theresa May's Chequers proposals for the future EU-UK economic relationship, which are hugely unpopular with Brexiteers, was misplaced.
Such an arrangement would all but end May's chances of securing free trade deals with other countries.
The UK and the European Union have yet to strike a deal on how Brexit will work, with less than six months to go before the UK leaves on 29 March.
The prime minister briefed ministers on negotiations yesterday amid speculation that the government is moving closer to a deal with Brussels.
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The DUP now stands in the way of the Prime Minister's plan to allow a number of checks between Northern Ireland and Great Britain in a bid to convince Brussels a UK-wide backstop is acceptable.
European Union leaders have a two-day summit starting Wednesday to assess the progress in the talks and if there is no breakthrough there, another summit could be planned for November.
The UK is expected to come up with new proposals as an alternative to the "backstop" put forward by the European Union - which the government has rejected, saying it would threaten the integrity of the UK.
And the end to portability legislation in the United Kingdom isn't the only warning put out by the government in this latest batch of dossiers, with fears over the smooth running of the Eurostar between London and Paris along with Northern Ireland's access to electricity also being published.
EU Brexit negotiator Michel Barnier on Wednesday rammed home that - while the bloc was looking at ways to carry out checks on many goods away from the actual frontier - animal and animal products would have to be screened on the border.
"She will not have DUP support regardless of whether the government tries to bribe, bully or browbeat us into accepting it", Wilson also said.
He hit out the "not so subliminal bullying" by Tories opposing her strategy in the middle of negotiations and also criticised International Development Secretary Penny Mordaunt, who declined to give the PM's plan her explicit backing when asked earlier this week.
Meanwhile, shortly after the meeting began, the Democratic Unionist Party (DUP) leader, Arlene Foster, said that Theresa May and her cabinet "have assured me of their unionism".