The Northern Ireland party props up the Conservative minority government and the Prime Minister will be relying on DUP support to get the deal she is presenting to ministers tonight through Parliament.
However DUP deputy leader Nigel Dodds has said his party will not support the agreement “on constitutional grounds” as it would leave Northern Ireland subject to rules and regulations set “in Brussels with no democratic input” from Belfast.
He said: “We object to that on constitutional grounds that our laws would be made in Brussels, not in Westminster or Belfast.
“That is the fundamental red line.”
Mr Dodds added that any regulatory checks between the UK and Northern Ireland “would certainly be a breach of the PM’s pledges to the people of Northern Ireland (and) the pledges that she made to the people of the United Kingdom”.
Asked if the DUP would oppose the deal in Parliament he said: “We at that stage will look at all of this.
“I think there are many people in the Conservative and Unionist Party who will not stand for this kind of approach either.”
When pressed on whether the Prime Minister’s Brexit deal could spell the end of the confidence and supply agreement between the DUP and the Torys, Mr Dodds said his party will see what “transpires in the course of the next few days.”
He said: “The confidence supply arrangement is one we have in terms of making sure the government delivers on a stable government and delivers on Brexit and the other priorities that we have.
“We’re very clear about what Brexit means.
“Let us see what transpires in the course of the next few days and weeks.
“We are very focused on delivering a proper Brexit for the United Kingdom and Northern Ireland and we will ensure that happens.”
Meanwhile, the DUP’s Brexit spokesman, Sammy Wilson, reminded the Prime Minister of promises she has made in order to maintain the strength of the union.
He told the BBC: “These are promises which she made because she recognised that the integrity of the United Kingdom was important.
“She has made them time and time in the House and to us privately and to the public.”
Prime Minister Theresa May is holding one to one meetings with her Cabinet ministers tonight as she hopes to persuade them her deal is the best option for the United Kingdom.
However a number of leading Brexiteers, including Boris Johnson, have said they will vote against the divorce agreement.