Her intervention came as Mrs May met key members of her cabinet in Downing Street to brief them on the progress in the Brexit negotiations.
However Brexiteers - including UK Brexit Secretary Dominic Raab - are insisting any arrangement which would see the UK effectively remain part of the customs union while negotiations over a free trade deal take place must be strictly time-limited - something the EU has been resisting.
It comes as the deadline looms for a deal between London and Brussels.
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.
Both sides have made positive signals in recent days though also indicated they were still short of a deal, which would define the divorce terms and include an European Union declaration stating that it would seek the closest possible ties with Britain after Brexit ranging from trade to security to research. 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?
The DUP are now refusing to back any proposal which includes significant regulatory checks between Northern Ireland and the rest of the United Kingdom, fearing this would undermine the union.
British and European Union negotiators are understood to have agreed in principle to an all-UK backstop plan to avoid a hard border in Northern Ireland that would remove the final major obstacle blocking a withdrawal agreement.
"We are not there yet".
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But diplomats told Reuters hopes were high that a breakthrough on the Brexit deal would be made on Monday.
"Why give ourselves this problem in a field of the global economy where we are globally preeminent?" he said.
As that departure date creeps closer, pressure on May from various directions is intensifying.
"Clearly Number 10 are negotiating a "backstop" that makes the United Kingdom a permanent European Union colony", former foreign minister Boris Johnson warned on Wednesday.
The DUP has 10 MPs, although Ian Paisley can not vote in the Commons until November 20 after being suspended for failing to declare two family holidays paid for by the Sri Lankan government.
The parliamentary arithmetic is hard for May who commands a majority of only 13 lawmakers including the DUP.
But he said that checks on animals and animal food products passing between Northern Ireland and Great Britain would have to increase tenfold.
Barnier warned that companies will have to adjust even if there is a Brexit deal.