EU leaders are due to meet for dinner in Brussels next Wednesday and hope to agree a withdrawal treaty with Britain that Barnier said was 80-85 percent ready but on which obstacles remain, notably on how to keep the new EU-UK land border with Northern Ireland from reviving conflict in the British province.
There have been faint signs of progress amid reports that the two sides are now working on a single text of a divorce agreement - rather than making counter-proposals.
DOWNING Street has played down expectations of an agreement on the UK's withdrawal from the European Union at a summit next week, warning that "big issues" remain to be resolved.
DUP MEP Diane Dodds, who also took part in the meeting, said any type of trade barrier between Northern Ireland and the United Kingdom would be "disastrous".
But Foster refused to consider such a compromise on Tuesday, saying: "What we said to Barnier is checks of themselves are symptomatic of something different, so we only need checks if Northern Ireland is following a different regulatory regime to the rest of the UK".
The joint survey by the University of Edinburgh and Cardiff University found that 87 per cent of the overwhelmingly unionist advocates for leaving the European Union believe the collapse of the peace process is justifiable if Brexit is delivered.
Under the European Commission's "backstop" plan for the Irish border, customs and Value-Added Tax checks would be carried out using existing customs transit procedures, to avoid the need for physical inspections at the border, he said. It is a negative negotiation.
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Mrs May is thought to be trying to unlock the negotiations with new plans for a "backstop" to avoid a hard Irish border.
That could destroy relations between Mrs May and the DUP - which has warned it has a "blood red" line on the issue.
The ten Unionist MPs prop up Theresa May's government, which has no majority, as part of a confidence and supply deal in which they are relied on to vote through the government's Budgets.
At his latest appearance in parliament, where divisions over how to leave the European Union were on display, Raab moved to downplay one of the thorniest parts of the talks - a so-called backstop arrangement to prevent the return of a hard border between the British province of Northern Ireland and European Union member Ireland.
The EU's top civil servant Martin Selmayr is said to have led discussion of a document on the consequences of no-deal - which the bloc has apparently decided not to publish for fear of derailing negotiations.
"That's why the backstop proposed by Barnier is unacceptable to us". If the DUP again voted down any regulatory differences whatever, we are left with No Deal, unless the DUP concede something.