Senior figures close to Mr David Trimble say he has "almost certainly fought his last election as leader" of the Ulster Unionist Party.
Yesterday the UUP suffered more reverses at the hands of the Rev Ian Paisley's Democratic Unionist Party in the Northern Ireland local elections, while Sinn Fein gained 34 council seats to rise above 100 seats for the first time. The UUP lost 31 seats in all, while the DUP won 40 extra seats.
As Mr Trimble played down the scale of his party's losses, well-placed party sources said he could still face a direct leadership challenge - from the Rev Martin Smyth or Mr Jeffrey Donaldson, or both - at the rescheduled annual meeting of the Ulster Unionist Council on Saturday week.
Some of Mr Trimble's supporters think he should stay on to conclude the negotiations which will determine the fate of the Belfast Agreement. At some point thereafter - whatever the outcome of the negotiations - they envisage Mr Trimble making way for an alternative leader who might re-unite his party.
These pro-agreement sources calculate that the party will reject any attempt to reopen the leadership question in advance of Mr Trimble's July 1st deadline for a substantial IRA move on decommissioning, or his resignation as First Minister.
The Rev Martin Smyth has yet to decide whether to challenge for the leadership of the party, and there is speculation that Mr Donaldson might enter the fray. Sources close to the Lagan Valley MP say he would be "extremely reluctant" to challenge Mr Trimble, adding that "he hasn't ruled anything in or ruled anything out".
Meanwhile, there was comfort for the SDLP and its leader Mr John Hume in the final results. Sinn Fein, at 21 per cent, was two percentage points ahead of the SDLP in the local elections. However, the SDLP dropped only three seats from its 1997 council figure of 120 seats.
The British and Irish governments are very concerned about the fallout from the election. Dublin and Northern Ireland Office sources say there is unlikely to be any set-piece start to negotiations on Monday week, and that Mr Trimble's meeting in London yesterday with Mr Tony Blair effectively began this latest talks process.
Before that meeting the newly elected UUP MP, Mr David Burnside, claimed an announcement was imminent that the IRA had permanently sealed one of its arms dumps.
"The Unionist community is not prepared to accept any more concessions. Gerry Adams is going to tell Mr Blair that one IRA arms dump has been permanently sealed to try and get a fudge on July 1st," Mr Burnside said. "But it is a con job which won't wash. The Ulster Unionist parliamentary party is in no mood to compromise." Sinn Fein Assembly member Mr Gerry Kelly replied: "My first reaction is that this guy is making the stuff up as he goes along. What would he know?"