Although the parties sent out contradictory messages on the chances of success, an apparent breakthrough on a key issue was reported at 6pm by John Taylor MP, the Ulster Unionist Party deputy leader.
Mr Taylor declared: "We are moving in the right direction. We've now more or less agreed the north-south link, but we've got to get a strong east-west link agreed also, and then the whole issue of the assembly, its structure and decision-making procedures."
The north-south link - the arrangements for a new cross-border institution connecting Belfast and and Dublin - has so far proved the most contentious issue of the talks. Many believe that agreement on the issue would prove the vital key to agreement elsewhere in the talks.
Mr Taylor's assessment was endorsed by the SDLP deputy leader, Seamus Mallon, who said: "It may well be moving in that direction. I think there's going to be a deal. I hope it will be tonight." The Ulster Democratic Party leader, Gary McMichael, added: "It looks as though that nut has been cracked."
Agreement in the talks, though vital, represents only the beginning of an arduous political process which will entail placing the agreement before the electorate for endorsement for referendums in Northern Ireland and the Republic.
Success will also depend on all the elements involved receiving the approval of their grassroots. There has already been some comparatively minor splintering on the issue within Sinn Fein and the IRA; the calculation of Sinn Fein president Gerry Adams will be that most of the potential dissidents have now gone, and that the accord can be successfully sold to the vast majority of republicans who remain.
But considerable dissent is already visible on the Unionist side, where the Rev Ian Paisley, leader of the Democratic Unionist Party, is vowing to smash whatever agreement should emerge. Last night, in a classic Paisley scare story, he announced that an agreement would mean officially sanctioned paramilitary policing - "You're going to have gunmen in uniform being policemen," he declared.
The Ulster Unionist Party leader, David Trimble, last night left the talks to brief his party executive on the progress of discussions. He had placed the executive on standby for an emergency meeting at party headquarters.
He was clearly concerned to cover himself against allegations of reaching an agreement without properly taking soundings from the Unionist grassroots. Such accusations have in the past proved damaging, and on occasions politically fatal for previous Unionist leaders.
The first official admission that the talks might not be complete by the midnight deadline came, bizarrely, from Kentucky, where President Clinton's spokesman, Mike McCurry, said the President had been told by Mr Mitchell that "agreement is near but the talks will probably go past the deadline".
Last night, the two governments were planning to produce another paper in succession to that delivered to the parties by talks chairman George Mitchell earlier this week. This would represent a near-final version of an agreement.
Tony Blair's official spokesman said the Prime Minister believed that agreement could be reached by the midnight deadline: "I think he feels there is an irresistible force and an immovable object and the irresistible force will prevail."
Gerry Adams said his party had submitted amendments and texts on areas of difficulty which included British constitutional change, the shape of all-Ireland institutions, policing, prisoners and other issues.
Monica McWilliams, leader of the Women's Coalition, said tensions inside the talks were running high but insisted a deal was possible by the deadline or soon after. She added: "We still believe that we are going to make this deal. Tensions are running very high at the moment."
Rev Paisley's deputy, Peter Robinson, added: "We are not a part of this process because it was very clear the Government wanted to do a deal with terrorists, who were busy busting kneecaps, shooting and even bombing. They wanted to do a deal with terrorists in order to silence their guns."