Democratic Unionists say a customs border in the Irish Sea is a threat to peace.
The party is meeting for its annual conference in Belfast today.
Last year's meeting saw cheers welcoming the attendance of the then Conservative Party back-bencher Boris Johnson.
But DUP relations with the new British prime minister have changed radically in the past year.
Brexit has both united and divided Mr. Johnson and the DUP.
The two-year-old alliance that gave his party influence at Westminster and special funds for Northern Ireland has been badly strained by Brexit negotiations and in particular Mr. Johnson's withdrawal deal.
The rival Ulster Unionist's Steve Aiken said the concern was always that the Conservative Party would throw Northern Ireland under the bus over Brexit - and now he claims they have.
However, despite Brexit pressures, a lack of devolved government at Stormont, and changes to the laws on abortion and same-sex marriage - which have long been opposed by the DUP - senior sources in the party claim the mood is good.
DUP MP Jeffrey Donaldson said they cannot accept the Brexit terms being proposed by Mr. Johnson.
"Where we have to accept a customs border in the Irish Sea, which will increase the cost of doing business for Northern Ireland businesses - particularly in our biggest market in Great Britain.
"That is unacceptable: it will be highly damaging to our economy, it will destabilise the peace process in Northern Ireland because prosperity and peace go hand in hand".
He added: "We want to go forward, we want Brexit to happen, we recognise and support the fact that the people of the United Kingdom voted for it."
"We want to implement it in a way that keeps the United Kingdom together.
"We leave as one country, the union is important to us and the prime minister needs to understand that: the union comes first."
