The DUP has warned Theresa May to “keep her side of the bargain” on Brexit after the party’s 10 MPs withheld their support in votes on Budget measures.
Mrs May insists her draft EU withdrawal deal, which MPs will vote on next month, is the right one.
She remains under pressure from Tory MPs to seek concessions from the EU.
The DUP, which props up the government, said it was sending the PM a “message” over her plan to “separate” Northern Ireland from the rest of the UK.
The party’s decision to abstain on a series of amendments to the Finance Bill on Monday night – as well as support an amendment proposed by Labour – was seen as a gesture, rather than an attempt to influence policy.
European leaders are set to sign off the draft withdrawal agreement and framework of future relations in Brussels next month.
Mrs May’s new-look cabinet meets on Tuesday for the first time since a number of ministers resigned last week, after they said they could not support the deal.
But the prime minister continues to be the target of backbench critics within her party, who appear intent on forcing a confidence vote on her leadership.
If the chairman of the 1922 Committee of backbench Conservatives – Sir Graham Brady – receives letters from 15% of the party’s MPs, a secret ballot is triggered.
A source has told the BBC they have not given up hope of reaching the required threshold of 48 letters.
Not everyone who had pledged to send in letters has done so, the source said. As of Monday evening, only 26 had publicly confirmed they had.
Ministers from the remaining 27 EU countries have met in Brussels to work on the political declaration setting out their future relationship with the UK.
Both the UK and EU have indicated that the draft withdrawal agreement reached last week – including the controversial “backstop” plan to avoid the return of customs posts on the Irish border in the event no new trade deal is in place – is unlikely to be changed.
But the BBC’s Laura Kuenssberg has been told by senior Brexiteers that discussions with Number 10 earlier were “constructive”, while a minister also said to “expect a little movement”.
As it stands, there appears to be a majority in Parliament against the deal.
The Democratic Unionist Party has made it clear it cannot support the agreement as it stands, saying the backstop would result in new regulatory barriers between Northern Ireland and the UK.
The party has been propping up Mrs May’s government in key votes in the House of Commons since last year’s inconclusive election result, via a “confidence and supply” arrangement.
But on Monday its MPs abstained on a series of votes on the Finance Bill, legislation needed to implement measures in last month’s Budget, and voted with Labour on one occasion to cut the government’s majority to just five.
It sent a “political message” to the PM over her willingness to “separate” Northern Ireland from the rest of the UK, Brexit spokesman Sammy Wilson said.
The DUP says this is not the end of the arrangement of so called “confidence and supply” agreement, where the government can formally rely on support from the Northern Irish unionists’ 10 votes.
But the fabric of that arrangement is certainly torn… and once faith is broken between the two, it’s hard to see how it could be restored.
Remember, there’s a really straightforward reason why this matters so much. Theresa May does not have enough votes on her own to pass the Brexit deal.
The partnership with the DUP was set up to try to make sure she could. If it collapses completely then her central task becomes yet more seemingly impossible, even if those 48 letters never come.
A DUP source told the BBC its MPs were “sending a message to Theresa May that if she wants to continue down the road of the withdrawal agreement and its effect on the union then there will be repercussions in the Commons”.
Mr Wilson, one of the party’s MPs, told the BBC’s Newsnight that they had “shown their displeasure” at the fact Mrs May was prepared to separate Northern Ireland economically and constitutionally from the rest of the UK.
Their message to the government, he said, was: “Look, we’ve got an agreement with you but you’ve got to keep your side of the bargain, otherwise we don’t feel obliged to keep ours.”
Mrs May has insisted the agreement reached is in the national interest.
But ministers have bowed to demands from MPs to publish an assessment of the economic impact of the draft withdrawal agreement negotiated by Mrs May compared with staying in the EU.
The analysis, which will also include modelling on a no-deal Brexit and a basic free trade agreement versus the status quo, will be made public before MPs decide whether to reject or accept the terms of the UK’s exit in the crunch Commons vote.
Labour and Tory MPs who back a further referendum on Brexit said the public had a right to know the “full facts” about the cost of leaving the EU.
The EU’s remaining 27 members could agree the final draft political declaration on future relations with the UK on Tuesday.
However, in a sign on tension on the EU side, Spain has said it will not agree to the draft Brexit withdrawal deal without clarity over how talks on the future status of Gibraltar should be handled.