The Democratic Unionist Party has said it will be supporting the government in a series of crucial Brexit votes over the next two days at Westminster.
MPs are due to debate 14 amendments to the EU Withdrawal Bill made by the House of Lords.
The bill underpins the government’s Brexit strategy.
Prime Minister Theresa May could face a possible backbench revolt and she has urged potential Conservative rebels to support the government.
Mrs May can count on the support of the 10 Democratic Unionist Party (DUP) MPs – secured as part of the confidence and supply deal – but not some Tory backbenchers who voted to remain.
If enough of them side with the opposition, the prime minister could lose some key votes.
The most important is the Lords’ plan to give Parliament a meaningful vote on the final Brexit deal.
Lose that and Mrs May could lose control of the Brexit negotiation. That vote is due later on Tuesday.
The DUP’s Westminster leader Nigel Dodds said he had been in intensive discussions, not just with the Conservative Party but with Labour as well.
He told BBC NI’s Good Morning Ulster: “My sense is that people are coming together, not only the Conservative benches, but also talking to Labour colleagues last night.
“The sense is that they are saying, ‘We can’t possibly be seen to be voting against Brexit because the referendum result needs to be delivered’.”
Mr Dodds said that many of their constituents in the north of England voted overwhelmingly to leave the European Union.
“What the government is keen to resist is a situation where, by means of a legislative amendment, some Tory rebels succeed in doing only one thing which is to make the Prime Minister’s negotiating position much more difficult,” he said.
Mr Dodds said the focus should be on delivering a Brexit that works for the UK, the EU and for Northern Ireland.
What is the EU Withdrawal Bill?
It is the legislation aimed at ensuring the UK has a smooth transition out of the EU.
It will repeal the European Communities Act, which took Britain into what was then the European Economic Community, meaning EU law is no longer supreme in the UK.
And to avoid a sudden “cliff edge” on Brexit day, 29 March 2019, it would also convert existing EU law into UK law so the government and Parliament can decide at a later date which bits they want to keep or change.
The bill has also become of the focus of several attempts by MPs and peers to change parts of the government’s approach to Brexit.
The legislation is now back before the House of Commons after a total of 15 defeats by the House of Lords.
The key dates ahead on Brexit