Theresa May might have to be replaced by the Conservative party to ensure its confidence and supply agreement stays intact, the Democratic Unionist Party's Brexit spokesperson has warned.
Sammy Wilson claimed that his party vote down the Budget later this month to "pull the government back into keeping its promises".
Ms May relies on the support of the 10 DUP Westminster MPs in key votes because she does not have a majority in the House of Commons.
But the Northern Irish party have been issuing regular warnings about the prime minister's Brexit plans and have urged her to change course.
If the DUP voted against the Budget, the government would face possible defeat, which could in turn lead to a no-confidence vote.
"That may lead to a different leader. But that's not a question for us, we're not members of the Conservative Party,” Mr Wilson told Sky News.
The DUP's Brexit spokesperson added: "That's up to the Conservative Party to decide whether there is someone else who can heal those wounds and take the party in a different direction, which would ensure that the agreement could stay in place."
With less than six months to go before the UK leaves the European Union on 29 March, a deal is yet to be struck on how Brexit will work.
A key issue to be agreed is how to prevent there being new border checks between Northern Ireland and EU member, the Republic of Ireland.
The EU has suggested that Northern Ireland effectively to remain in the single market and the customs union to avoid the need for customs checks until there is a final free trade deal between the UK and the EU.
But the DUP has said it will not tolerate this.
Ms May insists such an arrangement must apply to the whole of the UK to avoid the creation of a "border in the Irish Sea" between Northern Ireland and the rest of the UK.
Following three days of talks with key figures in Brussels, Arlene Foster, the leader of the DUP, said she could not accept the EU proposals as they stood.
"The Prime Minister is a unionist. Many of her cabinet colleagues have assured me of their unionism," she said. "Therefore, they could not in good conscience recommend a deal which places a trade barrier on United Kingdom businesses moving goods from one part of the Kingdom to another."
The Independent has launched its #FinalSay campaign to demand that voters are given a voice on the final Brexit deal.