Space is being provided for Mr David Trimble and for the Ulster Unionist Party as the British and Irish governments seek to revisit the terms of an arrangement that would bring the Belfast Agreement into effect.
Negotiations between the political parties, including the UUP and Sinn Fein, will resume in Belfast this week as they consider proposals put forward by Mr Trimble before he left for the United States.
In his absence, the deputy leader of the UUP, Mr John Taylor, along with Sir Reg Empey will represent the party in the discussions.
The Taoiseach, Mr Ahern, and Mr Tony Blair had a number of long conversations on the problems facing the Belfast Agreement during a weekend spent at the British Prime Minister's weekend home at Chequers.
Last night a Government spokesman said the political prognosis was not as gloomy as it had been earlier in the week.
He hoped when Mr Trimble returned to chair talks with the other parties next Friday they would be able to build on progress already made.
Last Saturday Mr Ahern pleaded with everyone in the peace process not to put Mr Trimble in an impossible position.
"I think the idea of unduly straining anyone's negotiating position is unlikely to lead to success," he said.
He also commented that forcing parties to do things against their will would damage the Belfast Agreement.
Pressure to make progress in establishing an executive is still being maintained by the two governments.
They appear to be determined that cabinet seats will be allocated in the first week of next month, to be followed by a formal handover of power "on or before June 30th".
This would be proceeded by a report from Gen John de Chas telain on the progress being made on arms decommissioning.
The parties engaged in the negotiations are seriously concerned at the worsening security situation in Portadown, Co Armagh, as the annual Drumcree march app roaches.
And a series of loyalist attacks on the Catholic community have added to the inter-community tensions.
Officials and politicians from the two governments will be fully engaged in efforts to move the process forward this week and in providing the kind of reassurances required by the UUP before they agree to naming the executive.
Given the internal party difficulties experienced by Mr Trimble in trying to "sell" the Downing Street formula last week, however, it is possible that slippage could take place beyond the first week of June.