Ulster Unionists, Sinn Féin, Alliance and the SDLP rounded on the DUP after it threatened to boycott a meeting which would have seen the Rev Ian Paisley and Gerry Adams in face-to-face talks at Stormont.
Northern Secretary Peter Hain attempted to play down the difficulties and postponed the meeting.
He called the problem over ministerial pledges and the timing of Sinn Féin's endorsement of policing "a glitch". He had expected a problem and forecast there would be more.
Mr Adams said Dr Paisley had gone back on his word and was "trying to reshape" what was agreed at St Andrews last week.
"People will be disappointed that Ian Paisley went back on what he publicly committed to do," he said.
Ulster Unionist leader Sir Reg Empey said the DUP was now involved in "panic politics".
SDLP leader Mark Durkan hoped Dr Paisley "would think better" of his "boycott" of the meeting with Sinn Féin.
David Ford, the Alliance leader, described yesterday's events as "shambolic".
However, the DUP was having none of the criticism and hosted a defiant press conference in Stormont's Great Hall. "The squeals from the opposition are the best proof we are succeeding," Dr Paisley said.
"We are teaching the British government a lesson, they will not pull the wool over our eyes."
Dr Paisley said he would hold the government to the letter of its written commitments and "would push it down their throats, publicly" if they attempted to do otherwise.
Gerry Adams referred to a general perception that the public was dismayed by the events at Stormont. Pointing to a possible solution Mr Adams said: "We have put forward our suggestions about the pledge of office so why doesn't he come along and talk to us? I certainly hope he does so speedily."
Mr Adams indicated he was prepared to meet the November 10th timetable set by the British and Irish governments.
"The two governments want Sinn Féin to respond and I have agreed to do that and will do. We will consult, it is ongoing and we will do as we always do, keep our pledges.
"I take people at their word and I listened very intently to what Ian Paisley said at the close of the St Andrews talks. I think particularly the words at the end of his remarks were spoken in a very genuine way," he said.
Ulster Unionist Party leader Sir Reg Empey warned it was obvious that part of the understanding between the British government and the DUP "has started to unravel".
Sir Reg added: "We had a nervous groom, a reluctant bride and a marriage of convenience - but we don't have a civil arrangement."
SDLP leader Mark Durkan referred to obvious difficulties over pledges of office and commitments to policing, but advised all involved to avoid any panic at such an early stage.
Meanwhile the DUP MEP Jim Allister voiced reservations about aspects of the St Andrews Agreement.
"We cannot even consider going into government with Sinn Féin in a situation where the IRA army council still exists," he said.
He publicly questioned aspects of the St Andrews deal and criticised what he saw as the lack of a default mechanism in the event of any IRA activity.
Later the DUP issued a statement issued in the name of the Assembly group. They welcomed "the progress made for the interests of unionism and the cause of democracy by the party's negotiating team at last week's talks at St Andrews".