Mr David Trimble has said he has no intention of resigning as Ulster Unionist leader. However, if his party fares poorly in local election counts beginning today, a leadership heave will be increasingly likely.
The Taoiseach, Mr Ahern, and the British Prime Minister, Mr Tony Blair, are due to discuss the fallout from the Westminster poll when they meet for a European summit in Gothenburg, Sweden, this week.
Sinn Fein and the DUP performed strongly in the Westminster election at the respective expense of the SDLP and the UUP. If those results are replicated as the local council results come through today and tomorrow, further pressure will fall on Mr Trimble in particular but also on the SDLP leadership.
Anti-agreement UUP MP, the Rev Martin Smyth, has signalled he could be a challenger to Mr Trimble when the Ulster Unionist Council meets on Saturday week.
Other potential opponents, such as the Lagan Valley MP Mr Jeffrey Donaldson and newly-elected South Antrim MP Mr David Burnside, have not declared their intentions. If the local results are as bad as the Westminster outcome, which saw the UUP drop from nine to six seats, then they could also be prompted to mount challenges.
Mr Trimble last night expressed confidence there would be no UUP "meltdown" in the local elections. "Don't lose your nerve," he urged UUP members.
The new DUP MP for North Belfast, Mr Nigel Dodds, has said the Belfast Agreement should now be overhauled. "Trimble has basically run out of credibility and he is now running out of votes. The writing is on the wall."
Mr John Hume and the SDLP leadership are hoping they can regain some of the ground lost to Sinn Fein in the Westminster poll, notwithstanding the likelihood that Sinn Fein will dramatically eat into the SDLP's share of local council seats.
Mr Hume described the Westminster result as a "blip". Asked about his own leadership, he said he was committed to the SDLP and his role in it.