Charles Kennedy's former deputy, Sir Menzies Campbell, is clear favourite to succeed him as Liberal Democrat leader.
Sir Menzies took charge when Mr Kennedy was forced out by MPs on Saturday night and immediately announced he wanted the job full-time.
A series of senior MPs have backed him amid calls for rivals to stand aside and avoid a damaging contest ahead of the May local elections.
But party president Simon Hughes appears poised to challenge him and home affairs spokesman Mark Oaten is also considering candidacy.
Splits over the future direction of the party means a contest could prove highly divisive.
Mr Hughes represents the party's left-leaning social democrats while Mr Oaten would be a champion of the economic liberals.
Like Mr Kennedy, veteran MP and former Olympic sprinter Sir Menzies, aged 64, is seen as a figure who could straddle the two camps.
There have already been recriminations over the way Mr Kennedy was treated by his Parliamentary colleagues.
Months of anonymous briefings culminated in the leak that he was receiving treatment for alcoholism - something he long denied.
Even then, Mr Kennedy tried to survive by calling a leadership contest as he publicly confessed to his drink problem.
Furious MPs responded by giving him an ultimatum to quit or face a mass frontbench resignation.
Mr Kennedy bowed to the inevitable, admitting the support he had received from activists had not been matched among MPs.
The former leader's 79-year-old father, Ian, hit out at the "plotters" who pushed out his son.
"This has nothing to do with drink or my son's leadership," he told The Mail on Sunday.
"This is to do with a bunch of political plotters in his party who wanted him out regardless of anything.
"None of them had the courage to put their names forward when he declared the leadership election because they didn't want to give him a chance. They wanted him out despite everything he has done for the party."
Prime Minister Tony Blair said the Lib Dems now faced a critical choice over the party's direction.
"They have reached a high-water mark of being able to be all things to all people in different constituencies," he said.
Dr Evan Harris, a science spokesman, said there was "significant pressure" for a contest.
"It is an opportunity for us to show where the debate in the party is going," he said.
The party's one member, one vote constitution means a ballot of the party's 73,000 members in a process lasting around two months.
Mr Kennedy called for the party's rank and file to have a say in the election of the next leader.
Asked by reporters outside his London home if he had enjoyed a good night's sleep, Mr Kennedy replied: "I'm feeling fine."
He continued: "I think the really important thing now actually for the party is that an awful lot of our members out there - and this is a voluntary organisation right across the country - feel very shut out of the decisions taken so far."
Mr Kennedy said it was important to ensure the new leader was "democratically elected" so that members were involved in the decisionmaking process.
"I think that the members feel that they want to have a direct input. They have tried very hard over the last few days and weeks to make their views known," he said.
"I just hope they get the opportunity to make those views known because they don't want to lose their active engagement." ..SUPL: