I caught up with her in Brussels and asked her if she thought the Prime Minister had got the message. However, the British government would be able to point to criteria under which the arrangement would be terminated, fulfilling the British desire for it to appear to be a temporary arrangement.
Such an arrangement would all but end May's chances of securing free trade deals with other countries.
The challenge for May will be in selling the formulation to the whole cabinet.
Foreign Secretary Jeremy Hunt insisted that ministers would not sign up up to any plan which compromised the territorial integrity of the United Kingdom by imposing a "border in the Irish Sea". No 10 said the meeting was an informal one, meaning no decisions were taken; the key political meeting before next week's summit will come on Tuesday at full cabinet, one day before the European council meeting begins.
The OBR said weaker economic activity and higher prices could result from a no-deal Brexit. Downing Street earlier warned there were "big issues still to resolve".
Commenting on the Irish backstop, Barnier said the EU's plan to keep Northern Ireland in the Single Market and customs union would help keep the border invisible - a goal of both sets of negotiators.
The European Union is doing all it can to ensure checks on goods moving across Northern Ireland's borders would be made "in the least intrusive way possible", for example on ferries, at ports or in factories of origin, he said.
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".
The support of the Unionist party is crucial to Mrs May, who agreed a "confidence and supply" deal with the DUP in the wake of losing her parliamentary majority in last June's snap election. They suggested that senior ministers including David Lidington, May's de facto deputy, Northern Ireland secretary Karen Bradley and chief whip Julian Smith would try to find a solution to the DUP's demands.
"In the next two weeks we'll be deciding what we're going to do and I think, in all honesty Tamara, that everything is on the table, and the implications of that are clear", he said.