The DUP has accused the government of preparing for a Brexit U-turn after the chancellor suggested another referendum would be a “credible proposition”.
The DUP has also insisted that it does not support the UK joining a customs union with the EU.
On Wednesday, chief whip Sir Jeffrey Donaldson hinted the DUP might be open to a customs union.
But on Thursday, he criticised “halfway houses” and “staging posts”, saying it was not the Brexit people voted for.
Meanwhile, his DUP colleague Sammy Wilson hit out at Chancellor Philip Hammond for suggesting another referendum would be a “credible proposition”, before signing off on a deal.
Speaking in the Commons on Thursday, Mr Wilson said: “Are we beginning to see yet the start of another U-turn by a government which has abandoned all of its promises to go forward with a no deal, to have no border down the Irish Sea and to ensure we leave the EU on 29th March?”
Labour has called for a permanent customs union with the EU and is in talks with the government about reaching a compromise.
In a statement on Thursday, Sir Jeffrey called on Prime Minister Theresa May to press the EU for changes to the withdrawal agreement, rather than “subcontract” the negotiations to Labour leader Jeremy Corbyn.
“Whilst the prime minister and her government may consider other options as halfway houses or staging posts, that is not the Brexit which people voted for,” he said.
“We will work in Parliament for the referendum result to be properly respected.”
The DUP MP added: “It is late in the day, but it is still possible to secure a deal which implements the referendum result and enables the United Kingdom to take back control of its trade, money, laws and borders.”
Late on Wednesday, MPs voted by a majority of one to force the prime minister to ask for an extension to the Brexit process, in a bid to avoid any no-deal scenario.
Earlier that evening, Sir Jeffrey said his party would have preferred a form of Brexit that enables the UK to negotiate new trade agreements with other countries.
“That’s part of the reason for Brexit and maybe a customs union might be a temporary staging post towards that objective,” he told BBC Newsline.
“We will wait to see what the prime minister brings before Parliament but we are very clear, we want a Brexit that delivers for all of the United Kingdom and that keeps the United Kingdom together – that is our objective.”
MPs have been debating legislation which would require Mrs May to seek an extension to Article 50 and give the Commons the power to approve or amend whatever was agreed.
Wednesday’s knife-edge parliamentary vote to ask the EU for a longer Brexit extension was on a bill brought by Labour’s Yvette Cooper.
It was fast-tracked through all Commons stages – a process that can take months – in one day and is now going through the Lords.
It will still be up to the EU to decide whether to grant an extension.
Meanwhile, Attorney General Geoffrey Cox said it was an “article of faith” that the UK must leave the EU to honour the referendum result.
The comments come a day after Mrs May said that she will ask the EU for a further extension to Brexit.
Talks between the prime minister and Jeremy Corbyn on Wednesday were said to be “constructive”.
It is understood that each party has appointed a negotiating team, and they are meeting before a full day of discussions on Thursday.
Mr Corbyn had said he was “very happy” to meet Mrs May, and would ensure plans for a customs union and protection of workers’ rights were on the table.
The DUP has supported the government in a confidence-and-supply pact since June 2017, after a snap general election.
But it is at odds with the prime minister and her Brexit deal, because of the Irish border backstop in the withdrawal agreement.
The party opposes the plan because if it took effect, it would lead to trade differences between Northern Ireland and Great Britain, which the DUP said poses a risk to the integrity of the union.
The UK is still scheduled to leave the EU on 12 April, unless the EU agrees to another extension.
But it is likely to demand that the UK takes part in European elections, which are due to take place on 23 May.
However, Mrs May said she wanted any further extension to be “as short as possible” – before 22 May so the UK does not have to take part in the elections.
Both the UK and EU have continued preparations for a no deal, in the event that a breakthrough cannot be reached in time.