The Alliance leader, Mr Sean Neeson, said last night he still believed there was a 50-50 chance of a result being achieved at the Hillsborough Castle negotiations.
Speaking as the Taoiseach and the British Prime Minister returned to Hillsborough yesterday evening, he commented: "It's really a question of sequencing and language. It's a question of guarantees, and I think it's also a question of a shadow period for the executive.
"There are opportunities there. It's a question of people grasping these opportunities. If it means going through the night to try and get a result, that must happen."
The Women's Coalition leader, Ms Monica McWilliams, also welcomed the return to Hillsborough of Mr Ahern and Mr Blair.
She said the parties needed this boost to "put the spirits back where they should be, just to keep the commitment there and keep moving on".
"It's still anybody's guess that we are going to make it, though nobody has given up," she added.
Mr David Ervine of the Progressive Unionists said he could not see a deal being reached soon unless Mr Ahern and Mr Blair were going to "force hands".
"That is the only way they will remotely come to a conclusion. It may not be a successful conclusion, but the only way they are going to reach a conclusion is to throw down the gauntlet."
He said he did not know how a way was going to be found through the decommissioning impasse.
"Frankly I wish that Tony Blair and Bertie Ahern could pull some rabbit out of a hat, which they have been unable to do so far."
He said while the "mood music" had been reasonable, nothing had been agreed.
"I don't think there's any one element that has been copper-fastened and that we could build upon."
Mr Gary McMichael, leader of the Ulster Democratic Party, said yesterday's IRA statement did nothing to address unionist concerns and "offers nothing positive to the political climate".