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".
She has come under growing pressure from Brexit-backing Tories to drop the plan agreed by the Cabinet at her country residence in July and instead seek a Canada-style free trade deal.More news: Mental Health in the Workplace conference takes place at County Hall, Maidstone
It highlights how Theresa May's "precious Union" has little meaningful support among the British prime minister's own supporters or those in other parties who regard themselves as unionist.
She added they should also remember that Parliament gave the British people the decision over Brexit, and following the 2016 referendum result "it is our duty to ensure that we leave".
Mr Baker told BBC Radio 4's Today programme that he was expecting Tory Whips to go to work on the rebels - but that around 40 of them would stand firm against her.
The EU and United Kingdom have agreed that these checks "cannot be performed at the border" and the EU proposes to carry them out "in the least intrusive way possible", he said.More news: Scientist warning over climate change and global warming - CBBC Newsround
"If we followed Mr Barnier's advice, my information is that those checks would become 100%, although with a veterinary agreement in a future trade deal, that might be reduced somewhat", she said.
But one European Union diplomat was upbeat, saying the divorce deal, or withdrawal agreement, could be concluded by Monday and that officials were working on a proposal to avoid Britain having to come up with a separate backstop plan as a possible solution.
Following the College of Commissioners meeting, two commissioners stressed the importance of continued UK/EU co-operation on security after Brexit. "There is a strong shared self-interest in finding a way of maintaining co-operation on security, if that proves to be possible". Let's hope that we are going to have a positive end.
Reports had suggested Mr Barnier would present a paper setting out new European Union proposals at Wednesday's meeting, but it is thought this has been delayed until closer to the summit date.More news: Brits brace for 'the other' royal wedding
They "will not tolerate a half-in, half-out Brexit" he said, amid reports Mrs May will break the deadlock over the Irish border by keeping the EU's present customs arrangements beyond the transition period in December 2020.
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