Charles Kennedy has rejected claims he is in denial over his political career, after senior MPs urged him to quit.
More than half of his 62 MPs told a BBC Newsnight survey that Mr Kennedy should go or said his position was untenable.
Twenty-one frontbenchers have signed a statement saying they will resign if he does not quit by Monday. Another four MPs are refusing to serve under him.
Mr Kennedy insists he has overwhelming support from ordinary party members and says he will not abandon his duties.
Mr Kennedy, who has admitted to a drink problem, says he is determined to contest a leadership election.
He urged the party's MPs to "reflect carefully on things" over the weekend and said it would be a "dereliction of duty" to walk away from his job.
Every candidate must be endorsed by 10% of the party's MPs
Whole party membership chooses leader
One member, one vote
Single transferable vote system - members list preferences and votes from least popular candidate reassigned to others until a winner emerges
Kennedy is automatically re-elected as leader if no other candidates stand
"I probably know more about the meaning of the word 'denial' now than most others. I can assure you I am not in denial," he told the Independent newspaper.
"My head is firmly screwed on as ever when it comes to rational political judgements."
But 25 MPs said in a statement: "We have indicated to Charles Kennedy that we would no longer be prepared to serve under his leadership after this weekend and wish to give him the next couple of days to reflect on his position."
Sarah Teather, senior local government spokeswoman and one of those leading the push, said she had "sympathy and respect" for Mr Kennedy, but hoped he would step down for the benefit of the party.
"The situation is completely unsustainable and untenable and it is damaging the party for Charles to have organised the leadership campaign in this way," she said.
'Quick and honourable'
In a separate letter, eleven members of his shadow cabinet told Mr Kennedy he has lost their confidence.
And a Newsnight poll found that a total of 33 Lib Dem MPs said Mr Kennedy should go or was in an untenable position.
Thirteen believed he should stay, while 16 did not express an opinion.
Former party chairman Matthew Taylor, a close friend of Mr Kennedy who ran his 1999 leadership campaign, said it was understandable that Mr Kennedy was finding the situation hugely difficult.
"But this is not a moment in which Charles can continue as leader and that is the overwhelming view of those closest to him," Mr Taylor told BBC Radio 4's Today programme.
Some critics are threatening to call a no-confidence vote when Parliament returns next week if Mr Kennedy refuses to quit.
But Jackie Pearcey, a Lib Dem councillor from Manchester, accused some MPs of losing track of the interests of the party.
"Us ordinary party members are seeing a group of very ambitious people fighting each other down in Westminster," she told BBC News 24.
Simon Hughes has not declared his intentions
And Chris Abbott, Lib Dem leader on Redcar Council in Cleveland, said: "It is the membership that elects the leader and we should be trusted to make the right decision."
Preliminary results from a YouGov poll for the Daily Telegraph suggest only 27% of Lib Dem activists think Mr Kennedy should stay. So far, 284 people have responded to the internet survey.
Mr Kennedy has called for a leadership election and will be re-elected automatically if no challenger emerges. So far no other candidates have come forward.
Sir Menzies Campbell, the deputy leader, and home affairs spokesman Mark Oaten say they will not stand against Mr Kennedy.
Party president Simon Hughes has yet to announce his intentions.
Lib Dem peer Lord Lester urged MPs to put aside personal ambition and avoid a damaging contest by inviting Sir Menzies to become leader.
But MP and former frontbencher Phil Willis said it was "nonsense" to think there was one candidate everybody would unite behind.
Mr Oaten said everybody should reflect over the weekend on what to do next.
He urged the party to unite ahead of the local elections in May and argued there was no need for a "nuclear option" on Monday.
"Colleagues should now give Charles time to prove himself, to show he has got on top of his problems," he told BBC News 24.
Mr Oaten added: "At the moment we are just damaging ourselves."