Barnier told small business leaders that the talks were "continuing intensively this week, day and night, with the aim. of having a deal within reach, if we follow through to the end of this negotiations, on October 17".
Among those due to attend today's War Cabinet are: the Prime Minister's effective deputy David Lidington; Jeremy Hunt, the Foreign Secretary; Sajid Javid, the Home Secretary; Liam Fox, the International Trade Secretary; Greg Clark, the Business Secretary; Michael Gove, the Environment Secretary, and Gavin Williamson, the Defence Secretary.
According to the Financial Times, two pro-Brexit members of her Cabinet were believed to be on the cusp of quitting in protest to the United Kingdom remaining within a customs union with the EU.
In a statement Mrs Foster, whose party props up the British government at Westminster, said the European Union plan would effectively mean imposing a trade barrier between the Northern Ireland and the rest of the UK.
She added that the plan for checks on goods was "a one-way turnstile, which could restrict trade from Great Britain to Northern Ireland" and said it was "the worst of one world".
Following three days of talks with key figures in Brussels, DUP leader Arlene Foster said Mrs May could not in "good conscience" accept the proposals now on the table from the European Union.
Without a time limit, critics say Britain could be tied to the European Union indefinitely unable to negotiate free trade deals with other countries. 'An terrible lot depends on the talks in the coming days'. Another summit in November is planned to close the deal.
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Selmayr, secretary general of the European Commission, has been tasked with coordinating preparedness to protect the EU from economic and political damage if Britain leaves the bloc on March 29 next year without a divorce deal in place.
As that departure date creeps closer, pressure on May from various directions is intensifying.
"She will not have DUP support regardless of whether the government tries to bribe, bully or browbeat us into accepting it", Wilson also said.
"But that's not a question for us, we're not members of the Conservative Party".
He added that the DUP could vote down the Budget but still support the government in a confidence vote, as long as it changed its approach to Brexit. She needs to keep either her own party onside or attract votes from the main opposition Labour Party.
Earlier this week EU officials expected that a possible new United Kingdom proposal on the Irish border issue would suggest having the United Kingdom remain in the customs union indefinitely.
A functioning Northern Ireland executive could have an impact on the final terms of any Brexit deal, she emphasised.