The British Prime Minister, Mr Tony Blair, and the Taoiseach, Mr Ahern, are believed to have an agreed strategy to try to force the Leeds Castle negotiations to "the point of decision" this weekend.
Senior Sinn Féin and DUP politicians appear deeply sceptical about Mr Blair's insistence that "an alternative way" forward will have to be considered if they fail to reach agreement by tomorrow on "acts of completion" and the basis for the restoration of the power-sharing government at Stormont.
As the talks continued over dinner last night, however, it emerged that Mr Blair and Mr Ahern were preparing to present position papers to the parties overnight or early this morning.
These would represent the understanding of both governments of the position of the respective parties - principally but not exclusively the DUP and Sinn Féin - on the outstanding issues to be resolved and the requirements on each side for the resumption of devolved government.
The Irish Times understands that if the parties fail to agree the terms of "the basic agreement" required by London and Dublin then Mr Blair and Mr Ahern will consider turning the tables in the negotiation by defining the terms of the agreement they consider available and/or acceptable.
Expectations of such a development had been fuelled earlier in the evening when the Prime Minister's official spokesman reflected Mr Blair's growing impatience to see the impasse broken. The spokesman said the two governments were "not trying to bounce the parties into an agreement they do not want to make." But he added: "We are not coming back to another session like this. You can't keep putting off the point of decision."
Mr Blair's spokesman declined to explain what would happen if the parties chose to do so, and insisted the Prime Minister was working and preparing for success.
They recognised, he said, that significant progress had already been made in earlier discussions and that all the parties "have approached this negotiation in a very constructive spirit". But insisting "we can't keep going round the same course" the spokesman said the agenda was unchanged from Mr Blair's "acts of completion" speech in Belfast in October 2002.
Confirming there were no plans or proposals for any round-table talks involving all the parties, the spokesman said the bilaterals between the two premiers and the individual parties would continue until Mr Blair and Mr Ahern made their judgment on what was on offer.
Last night's reports that Mr Blair and Mr Ahern are prepared to take the initiative and set the pace are consistent with earlier indications that Mr Blair was determined to force the Leeds Castle talks to the point of decision by putting any outcome - successful or otherwise - before a reconvened Assembly.
A number of parties have confirmed that this concept, or variations of it, have featured in their discussions with officials in recent weeks.
One recurring suggestion has been that Mr Blair might be prepared to "run the present negotiation into the wall" by "putting it up to the parties" and obliging them to vote for or against any deal on offer or - in the absence of agreement - for or against the terms of an agreement which would be acceptable to the two governments.
The potential strength of such a strategy was more immediately obvious in the context of a situation in which republicans had provided terms acceptable to London and Dublin but rejected by the DUP.
Unionist rejection in the Assembly would then point to the further implementation of the other outstanding issues of the Belfast Agreement, with Direct Rule augmented by the British Irish Inter-governmental Council, which could assume a more pro-active role in the protracted absence of devolution.
However, when pressed to say how such a strategy would work in circumstances where republicans were considered to have fallen short of what was required, senior British sources would say only that "it would still be open to the prime minister to call it".