It came as Mrs May's "inner cabinet" was briefed last night on plans for a no-deal Brexit amid reports that progress ahead of a crucial European Union summit next week had been slower than hoped.
Foreign Secretary Jeremy Hunt arrives in Downing Street, London, for a Cabinet meeting on Thursday October 11, 2018.
Barnier said Brexit would trigger the need for customs, Value-Added Tax and compliance checks with EU standards between Ireland and Northern Ireland in the event that a planned "backstop" were triggered because a future EU-UK trade deal was not sufficient in itself to ensure the land frontier was not a "hard border".
Sammy Wilson, the DUP's Brexit spokesman, warned the PM was pursuing "the road to parliamentary defeat" because his party would vote against any deal that included the proposed backstop, branded a "sell-out".
Asked by the BBC to offer her backing to Mrs May's plan, Ms McVey sidestepped the questions. No, we don't want a hard border between the north and the south. That will become the only land border between the United Kingdom and the bloc.
Why would a Unionist politician want to bring down a Conservative and Unionist government, lose the influence it has on that administration and risk the extra funding for Northern Ireland that the DUP received in exchange for agreeing to support the Tory minority government?
Such an arrangement would all but end May's chances of securing free trade deals with other countries.
"We are not there yet".
As the rhetoric from Belfast intensifies and the DUP doubles down on its opposition to any checks on trade between Britain and Northern Ireland, Sabine Weyand, the deputy to the chief negotiator, Michel Barnier, told a delegation of Northern Irish business leaders invited to Brussels this week that the deal on the table was "the best the European Union has ever offered any country in the world".
And following three days of talks with key figures in Brussels, DUP leader Arlene Foster said the Prime Minister could not in "good conscience" accept the proposals now on the table from the EU. 'An bad lot depends on the talks in the coming days'.
Just six months before Britain is due to leave the European Union, some other British officials have voiced more caution, saying "big issues" still lie in the way of any agreement. Another summit in November is planned to close the deal.
As that departure date creeps closer, pressure on May from various directions is intensifying.
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.
Arlene Foster, the DUP leader, noting how the PM was also a Unionist, said: "What is important for us is to say to her very clearly that any impediment on the two-way access in the United Kingdom single market would not be good for the Union or the economy of Northern Ireland".