The Sinn Fein chief negotiator, Mr Martin McGuinness, has expressed confidence a deal on policing, arms, demilitarisation and the stability of the political institutions will be reached in the aftermath of the elections.
His comments came as the DUP said it expected a "watershed" Westminster election result will force the British and Irish governments to allow it into negotiations on the future of the North.
Mr McGuinness said he had a "fair degree of confidence that there is enough wisdom around, enough sense around, and enough leadership around on all sides for us in the aftermath of the elections to resolve the outstanding difficulties".
The North's Minister for Education said he "expected" the British government to introduce major changes to the Policing Act to meet the demands of nationalists and republicans and to ensure legislation mirrored the original Patten report.
He stressed it was "vitally important' co-operation continued between the representatives of nationalists and republicans on the policing issue to ensure a new beginning. "It is absolutely vital that everyone sings from the same hymn sheet."
Mr McGuinness said he did not believe Mr Trimble's resignation as First Minister on July 1st would be necessary.
The DUP deputy leader said their canvassing showed "our target areas are all reporting significant gains for the DUP" and predicted "a major shift in unionist opinion away from the treachery of David Trimble".
Mr Robinson said if the election was "the watershed we predicted it might be" the party would have a strong mandate to enter negotiations, but this time it would be the voice of unionism.
"We'll be holding the steering wheel if we are in the driving seat as far as unionism is concerned - then the Ulster Unionist Party can't capitulate and offer further concessions," he said.
The DUP leader, Dr Ian Paisley, said the governments would have to include his party in negotiations even if its gains were comparatively modest. "There is such a thing as a ballot box and that ballot box will be heard in this election," he said.
"I believe even if we take two or three seats things will change, things have changed since [the] South Antrim [by-election]," he said.
Dr Paisley would not be drawn as to how the DUP would negotiate but said the party was committing itself to seven principles.
These included a refusal to negotiate with parties linked to paramilitary groups.
The party would also call for the exclusion of politicians "not committed to exclusively peaceful and democratic means" from the Executive. Paramilitary arms would have to be decommissioned before this bar could be lifted, he said.
The party would demand both a restructuring of the Assembly and that any relationship between the Executive and the Government be fully accountable to the Assembly, he said.
The UUP Westminster candidate for Strangford, Mr David McNarry, claimed the DUP had no plan to secure devolution and decommissioning. "The only thing the DUP will negotiate after the elections is who they rotate for their ministerial posts."
Commenting on Mr McGuinness's statement that Mr Trimble would not need to resign on July 1st, Mr McNarry said: "Clearly, Mr McGuinness and his friends must be preparing to decommission their weaponry post-election."