The Prime Minister knows the consequences if she walks away from her Brexit promise to unionists, the DUP has warned.
The party gathered in Mid-Ulster on Friday to brief members on the Brexit process, with leader Arlene Foster and her deputy Nigel Dodds among those present.
Brexit spokesman Sammy Wilson urged Theresa May to show EU negotiators “the door”.
“I am sure the Prime Minister is well aware of the grave responsibility which lies on her shoulders.”
Mrs Foster met chief EU negotiator Michel Barnier in Brussels earlier this week.
The DUP’s MPs and members of the suspended devolved Assembly at Stormont gathered at Portadown in Co Armagh to receive an update on the Brexit negotiations.
Its red lines for supporting the minority Government at Westminster in key votes include preventing the imposition of customs or trade checks between Northern Ireland and Scotland, England or Wales.
Mr Wilson said the Prime Minister should face down the EU negotiators.
He added: “We are simply reminding her, you are being torn at the moment between what we believe are your gut instincts and your sound principles on the union and at the same time the bullying, threatening behaviour of the EU.
“Go with your principles, go with your instinct, go with your responsibility to the people of the UK and show the EU negotiators the door.”
There have been suggestions the DUP could vote down the Budget at Westminster over its Brexit concerns.
Mr Wilson added: “We are serious about ensuring that the unionist people of Northern Ireland are not in any way going to be affected by the narrow vision that the EU negotiators have in protecting their European project at the expense of the unity of the UK.”
He said Friday’s party meeting involves “serious business”.
He added: “The serious business is how we get through these current negotiations, live up to our promises to be a unionist party, and protect the union.”