It would be difficult to exaggerate the immense importance and potential of tonight's summit meeting between Mr Blair and Mr Ahern in London.
After he last met the British Prime Minister, on the margins of an EU summit, the Taoiseach set out consciously and deliberately to counter a sustained British hype about the prospects for agreement in the multi-party talks. Reflecting on the obstacles then still to be overcome, Mr Ahern ruefully remarked: "I can't pretend that it's not the middle of March . . . If I am correct, a month today is Easter Sunday."
Tonight neither Mr Ahern nor his host will be able to pretend that Easter doesn't fall on Sunday week and that before then, by their own prescribed timetable, and for good or ill, the process is scheduled to have come to an end.
For this guest, Mr Blair will stand in greeting at the world-famous door, smiling dutifully for the cameras. Away from the lights the two men and their chief negotiators will assess the mountains still to be climbed if that historic agreement is to be achieved.
And the first of those mountains is for Mr Blair and Mr Ahern to conquer. Much is made of the pressures on other participants in this process, most frequently those on Mr David Trimble, the Ulster Unionist leader. But the heat, too, is on the two heads of government. For (astonishingly perhaps) there is no agreed British-Irish position as the talks move into their final week.
Irish sources had seemingly invested great significance in Mr Blair's lengthy discussions earlier this week with Mr Trimble. The whispered suggestion was that it fell to Mr Blair to find out Mr Trimble's bottom line on the issues which would spell success or failure.
However, after two meetings in four days, there is no anguished suggestion yet that Mr Blair has been putting the squeeze on Mr Trimble. And the truth appears to be that the Taoiseach still does not know Mr Blair's own bottom line on the issues, across all three Strands, still to be resolved.
They may not be resolved tonight, but as one source put it, this encounter must provide "the prime ministerial kick" to resolve them, and in amazingly short order. For in reality the British and Irish governments must establish their common line before Senator George Mitchell presents a draft agreement to the parties on Friday. Next to impossible as that might appear, sources yesterday seemed in no doubt that, should Mr Mitchell prove unable to present a draft before the weekend, the April 9th deadline will fall.
There have been hints during the past few days that the Irish might be reconciled to that. But it is acknowledged that Mr Blair, and seemingly Mr Mitchell, are determined there should be no slippage.
Although technically not involved in the "internal" Strand One, the Taoiseach will undoubtedly impress on Mr Blair the SDLP's bottom line that an executive heads up the proposed Northern Ireland assembly, and that it should operate, as does the talks process, on the basis of sufficient consensus.
The first tentative signals are emerging from the UUP camp that it might be prepared to consider this (although it would come as a profound shock to much of the party). However, Mr Trimble and his colleagues have survived their recent talks with Mr Blair apparently confident they can win the big argument over the scale and scope of the North-South Council.
There has been endless legal argument between Irish Government and Ulster Unionist representatives about the legislative and statutory basis of the proposed council. In crude terms it boils down to a question of whether it should have significant powers, and be capable of having a life of its own, for example, through the implementation bodies, which Dublin says it must, and which the UUP says is out of the question.
Should the council have its own "executive" dimension or should that be provided by Irish Ministers and Stormont departmental heads, answering back to the Dail and the assembly? Should the British and Irish governments have powers to intervene if the council is deemed not to discharge its functions? And should any overall agreement provide for a continuum of the North-South arrangements even in the event of the assembly's failure? This remains the great North-South divide.
The trick, according to some key players, will be to reconcile Mr Trimble's concept of a "voluntary" relationship between the assembly and the Dail (incorporating the principles of openness and accountability) with a job description allowing ministers a fair degree of flexibility for decision-making, free of day-on-day scrutiny by assembly committees which might well be designed to render the entire North-South relationship inoperable.
Some trick. But then, only one of the many Mr Blair and Mr Ahern must perform.