Sinn Féin has said it is unlikely there will be a deal in the talks at Stormont in the short term.
“We don’t see any urgency in the DUP approach to this,” the party’s Conor Murphy said.
Northern Ireland Secretary James Brokenshire is due to address the House of Commons on Monday afternoon to update MPs on what will happen next.
Mr Murphy said the likely pause in talks over the summer would not help.
Northern Ireland has been without a functioning devolved government since January, when the coalition led by the DUP and Sinn Féin collapsed over a green energy scandal.
Mr Murphy told reporters on Monday: “We’re unclear as to what the British secretary of state will say.
“He may well, by all accounts, issue some form of a holding statement.
“We said over the weekend we don’t see any urgency in the DUP approach to this and we don’t think it’s likely that there will be a deal in the short term because there is that lack of urgency.”
He added: “Now we find ourselves up against the 12th July, the atmosphere becomes so hostile that the DUP are even less likely to move on some of these issues,” he added.
SDLP leader Colum Eastwood expressed frustration at the lack of progress in the talks.
“It is utterly exasperating that after months of talks, the DUP and Sinn Féin continue to lock our politics into a complete stalemate. Kicking the can further down the road, will rightly be met with public anger and disappointment.
“As the secretary of state prepares to make his statement today, I urge him to ensure that direct rule is not the price that the people of Northern Ireland will have to pay for the political failure of the big two.”
Power-sharing talks between Stormont’s two biggest parties, the Democratic Unionist Party (DUP) and Sinn Féin, broke up on Saturday with no deal.
The legal deadline for the talks was last Thursday.
On Sunday, the DUP’s Simon Hamilton said Sinn Féin could not “demand a 10-0 win” in the talks and needed to “change its attitude”.
His party has said the talks could be sorted out within hours if Sinn Féin was prepared to compromise.
In January, the late Martin McGuinness, of Sinn Féin, resigned in protest over the DUP’s handling of an inquiry into the Renewable Heat Incentive scheme.
His party had demanded that DUP leader Arlene Foster step aside temporarily to allow an investigation into the scheme she set up, but Mrs Foster refused.
Over the past six months, and during two elections at Stormont and Westminster, the two parties have been deadlocked over a number of issues.
The most significant sticking points are disagreements over an Irish language act, same-sex marriage, a Bill of Rights and measures to deal with the legacy of the Troubles.
The secretary of state has the option of giving the parties more time to negotiate, calling another assembly election or reintroducing direct rule from Westminster.
On Friday night, Mr Brokenshire said the absence of devolved government in Northern Ireland “cannot continue for much longer”.