The DUP has sought assurances from Theresa May following the resignations of David Davis and Boris Johnson.
In the House of Commons, the DUP Westminster leader Nigel Dodds directly asked the prime minister to reaffirm her stance against the EU "backstop" position in the event of a failure to reach a deal on the UK's withdrawal.
Ms May said she still rejected the EU interpretation of the backstop which would mean regulatory realignment between N Ireland and the Republic.
“I’m happy to say that I continue to reject the protocol that was put forward,” she said. It would have effectively carved NI away from the rest of the UK and “remains totally unacceptable,” she added.
But one DUP MP last night raised a question mark over the long-term future of the confidence and supply arrangement if a new Tory leadership contest creates further destabilisation and weakening of the UK in the Brexit negotiations.
Sammy Wilson said he believed Ms May would survive but whether she could stabilise the cabinet "remains to be seen".
‘Increasingly difficult ’
The East Antrim MP said it appeared to be increasingly difficult to deliver the kind of Brexit his party wanted to see.
Speaking in relation to the departure of the Brexit secretary Mr Davis, Mr Wilson said: “From the details we’ve seen at present it seems, first of all, we’d be tied up to EU rules now and in the future; secondly, there would be input for the European Court of Justice; and thirdly, there probably will be a bill to pay to the EU.
“I think that in all honesty he could not have kept on supporting that.”
After Ms May's statement, former NI secretary Owen Paterson asked for the "drop-dead moment" when the UK would give up on the EU talks and go forward on the basis of World Trade Organisation rules.
Ms May replied that Mr Paterson had been involved in enough negotiations to know that giving a date was not a sensible move.