The Democratic Unionist Party has threatened to take serious action if it remains unhappy over the government’s Brexit plans.
Sammy Wilson MP said the party’s abstention on the agriculture bill on Wednesday night was a warning to the government.
Theresa May relies on DUP support in key votes because she does not have a majority in the House of Commons.
Mrs May is to brief key ministers on negotiations with the EU later.
Conservative MP Helen Grant said she believed the DUP was “bluffing” about withholding its support.
Mr Wilson said the party was unhappy with what it had been hearing about the Brexit negotiations.
Writing in Thursday’s Daily Telegraph, he said “briefings and leaks” suggested the UK might consider arrangements that could exclude Northern Ireland from the UK’s trade deals or lead to checks on goods arriving from Great Britain.
Speaking about the agriculture bill vote, Mr Wilson told BBC News: “It was a way of reminding the government that while our vote wasn’t important last night, it would be important some time in the future, and we would have no hesitation withholding it if we thought that was a necessary sanction to impose.
“It was a warning: ‘Don’t take us for granted, we’re in an agreement with you, but it’s a two-sided agreement.
“‘You keep your side, we’ll keep our side, you break your promises and we then don’t feel committed to keeping our side of the bargain.'”
He added: “If they (the government) decide to cave in to the unreasonable and unnecessary demands which are being promoted by Brussels, then we will have to consider whether or not they have kept their side of the bargain.
“If they haven’t, there’ll be consequences, and one of the consequences is the votes that we have promised to deliver for their domestic legislation will not be forthcoming.”
The agriculture bill passed its second reading despite the DUP’s abstention, which means it will now come under detailed scrutiny in committee.
Mr Wilson said that the confidence-and-supply agreement must be honoured by both sides, and that if Theresa May were to accept the EU’s current proposals for the Irish backstop, this would be serious enough for the DUP to refuse to vote with the government when it comes to the Budget.
“If the prime minister were to cave in to the demands that we know Michel Barnier is making… that’s serious enough, for the UK, for us to take the kind of action that we’re going to take, and that we have threatened to take.”
He said Mr Barnier’s demands included “that we would stay as part of the single market, our laws in NI would be made in Brussels, not London, that we would not be able to be part of future UK trade deals, that the ECJ would make decisions about the rules and regulations in Northern Ireland”.
“The ball isn’t really in our court,” he added. “The government has to contemplate the consequences of giving in to the demands which are being made from Brussels at the minute.”