The party's Brexit spokesman Sammy Wilson later explicitly warned the Government against doing a deal that kept Northern Ireland in the Single Market, writing in the Telegraph the party could not support "any deal which includes such economically and constitutionally damaging arrangements".
Full cabinet members concerned about the idea of an indefinite backstop include Andrea Leadsom, the leader of the Commons, and Esther McVey, the work and pensions secretary, who refused to specifically endorse May's Chequers blueprint for Brexit earlier on Thursday - although she insisted that she was "completely supportive of the prime minister".
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.
Instead she proposed Britain as a whole stay temporarily aligned with the EU's customs union until a wider trade deal is agreed.
McVey's formulation echoed that used on Tuesday by Penny Mordaunt, the worldwide development secretary, who said that while "the prime minister can count on my support" she did not know "where this is going to end up". 'An very bad lot depends on the talks in the coming days'.
Barnier warned that companies will have to adjust even if there is a Brexit deal. "There are big issues still to resolve".
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".
In addition, Northern Ireland would remain under large parts of single market regulations, requiring enhanced checks on products arriving from Britain, particularly agricultural goods.
One official close to Brexit talks said May never brings the cabinet together to tell them recent developments and so "it feels to me like the deal is practically done", the FT quoted the official as saying.
Mrs Foster, speaking after a third day of talks in Brussels, said the decisions made by the Prime Minister in the comings days will be "critical" for Northern Ireland.
The OBR said if there was no agreement on standards everything would have to be resubmitted for approval: "In a scenario where the United Kingdom and European Union are unable to agree to the continued mutual recognition ('grandfathering') of existing product standards and professional qualifications, all existing goods may need to be re-approved before sale and services trade would be severely restricted by the loss of market access".