Ahead of a crucial Stormont debate next Monday on the transfer of powers to the Assembly, Mr David Trimble and Mr John Hume have placed hope in Gen John de Chastelain's agency somehow breaking the deadlock over decommissioning.
The suggestion by the Tanaiste, Ms Harney, however that former US senator George Mitchell be invited back to Northern Ireland to find a way over the decommissioning hurdle has prompted a generally polite but lukewarm response.
As Sinn Fein and the Ulster Unionist Party continue to insist on the correctness of their diametrically opposed interpretations of the Belfast Agreement, the North's First Minister, Mr Trimble, and the SDLP leader, Mr Hume, turned to the decommissioning body as a possible way of solving the problem.
Mr Trimble said in Brussels yesterday that people should "not abandon hope" that the work being done by Gen de Chastelain could prove fruitful.
Mr Hume, speaking at Stormont, said the executive should be formed and the issue of paramilitary arms and explosives left to the decommissioning body. It was formed to specifically deal with the weapons issue to the satisfaction of all parties, and it should be allowed get on with its business.
While Gen de Chastelain has stressed his impartiality, senior SDLP sources are hoping that he will soon be in a position to make suggestions or issue a statement that could allow the executive to be formed without either Sinn Fein or the UUP losing face.
The Sinn Fein president, Mr Gerry Adams, said it was false to present the dispute about decommissioning as a row between the UUP and Sinn Fein. "It is about whether the Good Friday Agreement is going to be implemented or whether the UUP is going to succeed, through exercising a veto, in parking or reviewing, in other words renegotiating the agreement," he said in Cork.
Mr Trimble said it was too early to talk about bringing back the former talks chairman, Mr Mitchell, to break the logjam caused by the row over arms, although he agreed there was provision in the Belfast Agreement for the Tanaiste's proposal.
Mr Hume said he was prepared to look at any proposal, although he believed the parties should get on with the business of implementing the agreement. "I think the best way for the deadlock to be broken is for all parties to concentrate on their duty to implement the will of the people, and implement that agreement," he added.
The Northern Secretary, Dr Mowlam, is holding a series of meetings with the North's political parties this week in an effort to find a way out of the impasse. She is charged with responsibility for triggering the mechanisms designed to set up the executive by March 10th.
Dr Mowlam would not disclose whether when the time came she would insist Sinn Fein take its two ministerial posts in the executive ahead of some IRA decommissioning, or whether she would accept Mr Trimble's interpretation of the agreement and seek to exclude Sinn Fein.
There were still a number of weeks to decision-day and, rather than her using "sledge-hammer powers", she hoped the parties would themselves work and co-operate to solve the problem. Were she to pronounce one way or the other now, it could mean one party or another walking away from the process.
Dr Mowlam expressed reluctance to seek the direct assistance of Mr Mitchell again. "I know he's got a young family and he gave two years of his life here. So I'm reticent to ask, because he's such a good man he would come."
The Deputy First Minister, Mr Seamus Mallon, said Ms Harney's proposal appeared just to transfer the problem from the Assembly to another forum.