The Ulster Unionist deputy leader, Mr John Taylor, has said it is time to admit the Provisional IRA will not hand over weapons and Gen John de Chastelain's International Commission on Decommissioning should disband.
Mr Taylor said the majority of unionists would undoubtedly now oppose the Belfast Agreement if another referendum was held.
He was speaking as anti-agreement unionists began preparing for an Ulster Unionist Council meeting which they hope will force their leaders to withdraw from government with Sinn Fein until there is actual decommissioning.
The UUP annual conference will be held in Belfast tomorrow. Six motions will be discussed, including one on the current political situation.
It states: "Conference welcomes the political progress made to date; condemns ongoing paramilitary violence; reiterates the party's determination to achieve full decommissioning of terrorist weapons and calls on the Secretary of State to ensure the operation of the rule of law in Northern Ireland."
However, it is the UUC meeting, not tomorrow's annual conference, which will be crucial for Mr David Trimble's political future. Anti-agreement unionists have sent a letter to party headquarters - containing 100 signatures - requesting a meeting to discuss policy.
It is understood it will be held on either October 28th or November 4th. Mr Taylor said that while his party had done everything possible to help the Belfast Agreement, it was now clear there would be no decommissioning.
"It seems to me that after two years, the International Commission for Decommissioning is wasting its time. They wait in vain for IRA decommissioning. Perhaps the time has arrived when realism must prevail and Gen de Chastelain should return to Canada. The circus cannot continue indefinitely."
However, the Northern Secretary yesterday warned that if the peace process collapsed, local politicians would lose considerable power and London and Dublin would be increasingly intervening in Northern affairs.
He said no UUP politician had presented a credible alternative to Mr Trimble's policies and new policies or a new leader would not achieve decommissioning.
The SDLP Deputy First Minister, Mr Seamus Mallon, said while he did not believe the Assembly and the Executive would be suspended, such a move could mean the end of the peace process.
"A suspension would be very damaging to the political process and people should ponder what that would mean. People should be aware that it is not a move which would guarantee a continuation of the process we have created."
Mr Trimble blamed the crisis on the paramilitaries' failure to disarm. He would not be drawn on the forthcoming UUC meeting but said there would be plenty of opportunities to debate the issues at tomorrow's annual conference.
His party could not be expected to shoulder all the problems of the peace process. "You cannot expect unionists to carry the burden alone," he said.
UUP anti-agreement MP Mr Willie Ross said it was only a matter of time before Mr Trimble faced a leadership challenge.
"He is on the skids and he cannot survive. This call for a UUC meeting is clearly another nail in his coffin."
Mr Ross added: "I believe many people in the party now accept this agreement has not delivered. Therefore a change in policy is necessary. The agreement has run its course."
Pro-agreement UUP MP Mr Ken Maginnis said another UUC meeting would not be helpful. "It is blatant exhibitionism and selfish opportunism by people who do not know what they actually want."
However, Mr Ian Paisley jnr of the DUP said: "David Trimble has failed to recognise that he is responsible for the mess Ulster is in and is culpable for the damaged Union that we are now living in. Trimble should now know that even though he does not want to quit, it is time to quit."