DUP deputy leader Peter Robinson has said he will be surprised if the timetable for appointing shadow first and deputy first ministers is met.
DUP leader Ian Paisley and Martin McGuinness, Sinn Fein, are due to become shadow first and deputy first ministers on 24 November.
But the DUP insists a pledge of support for policing is in place before then.
Mr Robinson said the DUP would not back down and he also cast doubts on the timeframe of the St Andrew's Agreement.
Interviewed for BBC Radio Ulster's Inside Politics programme, he was asked if the ministers would be in place by 24 November.
"I would be very surprised because there seems to be every indication that Sinn Fein will not be ready," he said.
"As far as we're concerned, there will be no jumping first by the Democratic Unionist Party - David Trimble might have done that, the Ulster Unionist Party might have done that, Reg Empey might be have been pleased to do it, but the Democratic Unionist Party will not."
Mr Robinson did not deny there were concerns within the DUP about the St Andrew's Agreement, but he insisted these concerns were shared by the leadership.
Sinn Fein President Gerry Adams said the remarks were "entirely predictable".
"Sinn Fein is very conscious of the difficulties facing the DUP. But Ian Paisley will not overcome these difficulties by creating new ones," he said.
On Friday, the DUP published a four page brochure urging unionists to give their verdict on the St Andrews Agreement.
The document stated that the agreement was undoubtedly a better package than the Good Friday Agreement.
It warned in clear terms the consequences of rejection. It said these included a greater role by Dublin in the government of Northern Ireland.
It said this would be coupled with the possibility of Sinn Fein in the Irish government.
The party wants responses to its headquarters by 8 November.
Meanwhile, the Northern Ireland parties have been given until 10 November to respond to the St Andrews Agreement.
It was published after intensive three-day talks between the parties at St Andrews in Scotland.
If all goes to plan, a first and deputy first minister will be nominated on 24 November and the devolved institutions will be up and running by 26 March.