DUP leader Arlene Foster has said "huge decisions" will be made ahead of the potentially historic meaningful vote on Tuesday evening.
She is to meet with the prime minister ahead of the scheduled vote and told RTE decisions will be taken over the course of the day.
Her party's Brexit spokesman Sammy Wilson said the latest agreement between the EU and Prime Minister Theresa May "seems to fall short" of her promises but said the party would take the time to consider its next move.
He said they party was being careful not to give an indication of how it would move until they had fully considered the new documents and taken advice.
Mr Wilson also said the party would "not be adverse" to a delay to the scheduled meaningful vote.
Sammy Wilson was speaking after Theresa May announced "legally binding changes" to the withdrawal agreement.
Speaking to radio station LBC, East Antrim MP Wilson said: "We had made it quite clear we expected legally-binding changes which would ensure our government solely had control over any backstop, that those legally-binding changes would ensure that in the future arrangements with Europe we would have control over our trade, laws and money. And that those legally-binding changes would ensure the integrity of the union.
"I have got to say if you look at what the prime minister has said so far it seems to fall short of what she herself had promised. She is simply saying it reduces the chances of us being kept in the backstop.
Mr Wilson said he wanted to give "due diligence" to what changes had been made and they would take advice from the "best people" and listen to the Attorney General on what he says later on Tuesday.
"But we want to hear the views of others," he said.
He also said he could not understand why the government appeared to be rushing the deal through.
Asked if he was minded to not support the deal, Mr Wilson said they have been careful not to give any indication as to what the DUP may do late on Tuesday in the meaningful vote.
"We have simply said this is what we expect and if it does not deliver that it will not have our support."
Shadow Brexit secretary Sir Keir Starmer - an eminent lawyer - said he would be "surprised" if the Attorney General was able to change his advice on the deal.
Mr Cox's advice on the previous version of the deal could not rule out being trapped "indefinitely" in the backstop, the set of measures which would tie the UK closely to Brussels' rules and tariffs in order to avoid a hard border with Ireland.
Sir Keir, who called for Mr Cox to face MPs in the Commons, said: "Having studied the documents, I would be surprised if they are sufficient to enable the Attorney General to change the central plank of his December legal advice."
The changes did not include "a mechanism for unilateral exit from - or termination of - the backstop".
Meanwhile, Mr Cox dismissed as "b*****ks" a suggestion that he had been pressured into finding a way to change his legal advice.
Tory Jacob Rees-Mogg, chairman of the influential European Research Group of Brexiteer MPs, said the "Star Chamber" of lawyers assembled by the group - including DUP MP Nigel Dodds, Conservative veteran Sir Bill Cash and outside experts - was also examining the deal.
"My focus will be on whether the unilateral declaration is genuinely unilateral," he told BBC Radio 4's Today programme.