The DUP will review its arrangement propping up the Conservatives if the draft Brexit plan gets through Parliament, the DUP's chief whip has said.
The DUP's 10 MPs have supported the government on key votes, but is opposed to the Irish border backstop proposal.
Sir Jeffrey Donaldson said the DUP will vote against the draft Brexit deal.
But a unionist former president of the Ulster Farmers' Union said the DUP is out of step with its base.
The Irish border has been the main sticking point in the talks.
The UK and EU have agreed to a "backstop", which would see NI stay aligned to some EU rules if another solution cannot be found.
Sir Jeffrey told BBC NI's The View programme on Thursday that the party's immediate focus is what happens with the Brexit deal.
"That is the most immediate priority. Part of our agreement with the Conservative party is the Brexit situation," he said.
"So yes, if the Conservative Party decided, and were successful in getting this deal through the House of Commons, then absolutely, we will have to review our position with regard to the confidence and supply agreement."
But Ian Marshall, a former Ulster Farmers' Union president who sits in the Irish Senate, told the programme the DUP was out of step with its natural support base.
When Sir Jeffrey was told that the chairman of the Northern Ireland food and drink committee welcomed the draft agreement, while the Ulster Farmer's Union supported the backstop, he replied: "They are wrong".
Sir Jeffrey added: "I don't believe they have read the detail of this, they have not read the 500 pages.
"There are serious constitutional and economic implications of this deal for Northern Ireland".
Mr Marshall said the comments were "disrespectful".
"These are the industry captains of business in the agri-food sector in Northern Ireland," he told Mark Carruthers.
"These guys have read the document, have examined the document. I have read the document, I have looked through it.
"It's actually a very credible piece of work. It's a very complicated piece of work.
"But I think it's completely disrespectful to imply that those individuals tonight haven't read, or don't understand, this piece of work.
"I think he's got it horribly wrong."
Richard Hogg of Manufacturing NI told the programme that politicians should "get over yourselves".
"We need a deal of some sort. If we don't have a deal then it's all going to fall apart," he said.
"Manufacturers, we're quite a simple bunch of people. We just want to create jobs, create wealth and keep things going."
'Threat to union'
Earlier, the NI Secretary Karen Bradley said the deal was "good for the union" and urged MPs to support it, but DUP deputy leader Nigel Dodds said the prime minister had broken promises made to his party.
But Sir Jeffrey said that the implications of the prime minister's plan was that "Northern Ireland will increasingly be left behind".
He also denied media reports that the DUP will end its confidence and supply arrangement with the government unless Theresa May quits.
He said the DUP's deal was with the Conservative party, not Theresa May, and that much depended on what happened in days to come.
He said the DUP still retained influence at Westminster, in light of several cabinet resignations that cited concerns over "threats to the union" because of the backstop proposal.
"It is not the DUP who are lonely tonight - it's the prime minister," he added.
What's the latest?
The real spat among politicians is over the UK and EU's agreement on the Northern Ireland backstop.
It would see Northern Ireland staying aligned to some rules of the EU single market, if another solution cannot be found by the end of the transition period in December 2020.
It would also involve a temporary single custom territory effectively keeping the whole of the UK in the EU customs union - until both the EU and UK agree that it is no longer necessary.
Mrs May has said there was no deal on the table that did not involve signing up to the backstop - but that it is only an insurance policy.
"I know there are some who said I should simply rip up the UK's commitment to the backstop but this would have been an entirely irresponsible course of action," she said.
Labour has also said it will not approve the plan, with party leader Jeremy Corbyn saying the backstop proposal would create a "de facto border in the Irish Sea".
Mr Corbyn said it locked "Britain into a deal which it cannot leave without the agreement of the EU".
What has the Northern Ireland secretary said?
Karen Bradley has denied accusations that the political fall-out over the draft Brexit plan is a "car crash" and said the deal was "good for the union".
She was speaking in Belfast after meeting a number of business leaders to discuss what has been agreed by EU and UK negotiators.
"Nobody said it would be easy," said Mrs Bradley, adding that the majority of the cabinet is still behind the deal.
She gave Mrs May her full support, and said: "This is a woman who gets things done."
The Northern Ireland Secretary also appealed for "cool heads".
"The people of Northern Ireland when they see this deal will see it is a good deal for the whole of the UK and Northern Ireland, and I hope they tell their politicians that," she added.
Asked about whether there are question marks over the future of the government's confidence and supply deal with the DUP, Mrs Bradley said that was a "matter for the parties' chief whips".
What about the Northern Ireland parties?
Mrs May has faced a huge backlash from the DUP, amid suggestions of moves within the Conservative Party to force a no-confidence vote.
Sinn Féin vice-president Michelle O'Neill said Brexit was not an "orange or green issue" and that the backstop would protect the Good Friday Agreement, while the SDLP leader Colum Eastwood urged people to stay calm to give the deal space.
Stephen Farry, the deputy leader of Alliance said it is important that the business community speaks out more loudly in the coming days, as the deal offers them the best of both worlds.
You can read more reaction to the proposals from the business community here.
But Ulster Unionist leader, Robin Swann, said the draft deal had been "a monumental error of judgement on behalf of the DUP", which would have a devastating long-term impact.
What happens next?
An emergency EU summit is now due to take place on 25 November to agree the draft text.
After that, Mrs May needs to get MPs to vote for it. The BBC's political editor Laura Kuenssberg said that could take place in early December.