Charles Kennedy has come under sustained attack from MPs and peers after admitting his struggle with drink and putting his leadership on the line.
Mr Kennedy, who called a leadership vote on Friday, said he had been overwhelmed by support from the public.
He vowed to fight on as leader - despite calls for him to quit to clear the field for other candidates.
MEP Chris Davies said Mr Kennedy was a "dead man walking" and MP Nick Harvey said his position was untenable.
Ex-frontbencher Jenny Tonge accused Mr Kennedy of "destroying the party".
Mr Kennedy will be re-elected as leader automatically if no challenger emerges. So far no other candidates have put their names forward.
Potential candidates Sir Menzies Campbell, deputy party leader, and home affairs spokesman Mark Oaten say they will not stand against Mr Kennedy.
Simon Hughes has not declared his intentions
Party president Simon Hughes has yet to announce his intentions.
The Lib Dem leader - who has previously denied a drink problem - on Thursday admitted seeking "professional help" to beat the bottle.
On Friday, he told reporters there had been "quite overwhelming" messages of support following that dramatic personal statement.
"I'm very, very touched by that and that is a reflection of the mood generally," he said.
The Lib Dem leader said he had done the fairest thing by triggering a leadership contest which any of his colleagues could enter.
A survey by London's Evening Standard newspaper says 16 out of the 23 frontbenchers want him to resign.
Baroness Tonge and Mr Harvey are among those who want Mr Kennedy to face a confidence vote of MPs and peers when Parliament returns next week.
Former MP Lady Tonge said she had been "appalled, saddened, disgusted" by Mr Kennedy's statement.
She claimed he was using an "underhand" strategy of appealing to the sympathy of Lib Dem members to stay in his post.
Just as nobody would employ a "one-legged actor as Tarzan", they would not deliberately choose an alcoholic as leader, the former GP told BBC Radio 4's Today programme.
"Over several years parliamentary colleagues have been embarrassed, worried that he might be having too much to drink, worried that he might not turn up to something," she said.
Lady Tonge, who was sacked as a frontbencher by Mr Kennedy, suggested he was still "in denial".
"He is destroying our party if we are not careful," she said.
Mr Harvey branded the idea of him standing in a leadership election as an "absurd charade".
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 don't believe that a sort of Soviet Union-style mock election with one candidate is really going to lance the boil or resolve the issue in any way, shape or form," he said.
The leader of Lib Dem MEPs, Mr Davies, said Mr Kennedy's leadership was coming to an end.
"People are not going to vote for a party because they feel sorry for its leader," he warned.
Mr Kennedy has faced growing calls to quit as leader in recent weeks, with 11 frontbenchers saying they had lost confidence in him, in a letter which was never sent.
Lib Dem MP Sandra Gidley, who signed the letter, said: "Charles must think hard about whether he has the personal strength to fight the triple demons of the Labour Party, the Conservative Party and the drink problem."
But Paul Holmes, chairman of the parliamentary party, said Mr Kennedy was in "good fighting form" and determined to go on.