Sources in the party - whose 10 MPs are propping up the PM in power - have warned it would be "unacceptable" for Northern Ireland and mainland Britain to be "treated differently".
The flow of Brexit-centric headlines continues through the week, and the UK Times is out with notes on UK Prime Minister Theresa, who looks set to chain down her own Conservative party within the UK's parliament in an effort to push through a Brexit compromise.
He said the MPs "will not tolerate a half-in, half-out Brexit" after reports that Mrs May hopes to break the deadlock over the Irish border by keeping the EU's present customs arrangements beyond when the transition period is due to end in December 2020.
Losing the party's support in the Commons would mean possible defeat on the budget and a no-confidence vote.
Speaking earlier on Sky News DUP MP Sammy Wilson said he believed there was no way forward in the Brexit negotiations "unless the Prime Minister is prepared to kick back at this late stage on the belligerent demands we have had from the European Union on Northern Ireland".
The former Brexit Secretary has written to his colleagues predicting a "dire" result for the Conservatives unless the Prime Minister ditches her so-called Chequers proposal, which would see the United Kingdom follow Brussels' rules on goods and agri-foods.
- Treasury minister John Glen backed a previous prediction by the Bank of England that around 5,000 financial services jobs will have been shifted out of London by "Day One" on March 29.
Chief EU negotiator Michel Barnier
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.
Barnier has amended the EU's "backstop" plan to try to minimise checks on goods coming into Nothern Ireland and make sure they take place away from the border.
Selmayr meanwhile "provided a brief update on the state of play of the Commission preparedness work and recalled the importance for all stakeholders to prepare for all outcomes and at all levels".
British security commissioner Julian King said: "There are some issues that will need to be addressed in the context of a future partnership, including on security".
"But as far as security is concerned, it is very important in order to ensure the security of our citizens and safety for our countries to keep working together in the future".
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.
But Mr Barnier's comments suggest there is still a long way to go before the crucial issues are settled.
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