Mr Kennedy has been struggling to maintain his position as senior colleagues voice growing doubts that he has the energy and vision to tackle a Conservative Party invigorated by the ascent of David Cameron.
Yesterday, he was warned to raise his game by one of his closest allies, Tom McNally, who said that without a "radical" improvement in his performance, the leader could be toppled this month.
Last week, some disgruntled grassroots Lib Dems claimed an internet petition had raised more than 3,000 signatures from party members demanding Mr Kennedy quit.
Now it has emerged that Conservative activists are backing a rival poll calling for Mr Kennedy to remain in office, calculating that a weakened Lib Dem leadership will be beneficial to Mr Cameron's hopes.
Several Tories are encouraging people to visit the website via their internet blogs.
Among them is Iain Dale, the former chief of staff to David Davis, the Tory shadow home secretary and leadership contender.
"Someone has started a Save Charles Kennedy website petition which you can sign up to," Mr Dale urges on his website. "In fact, I would urge all your friends to do so rather quickly."
In a further humiliation for Mr Kennedy, however, the petition at www.webpetitions.com/cgi-bin/print_petition.cgi?99500307 has so far attracted only 32 signatures.
By contrast, the www.kennedymustgo.co.uk/ site run by former Lib Dem candidate Ben Ram claims to have collected more than 3,000 signatures, although the names remain secret and the figure is disputed.
Mr Kennedy has tried to dismiss doubts about his position by insisting he will stay on, but even his supporters accept that he has failed to quell MPs' doubts.
"Charles should have put an end to this nonsense by now, but he just hasn't hit hard enough," said one sympathetic MP last night.
Mr Kennedy's survival now appears to rest on the fact that none of his likely replacements have publicly declared themselves as challengers, fearful of being accused of plotting against him.
Simon Hughes, the popular left-wing party president, has gone as far as to publicly back Mr Kennedy.
Sir Menzies Campbell, the deputy leader, and Mark Oaten, the home affairs spokesman, are both staying tight-lipped to avoid suspicion of disloyalty.
But more and more Lib Dems are willing to go public with their complaints about Mr Kennedy's laid-back leadership style.
Lord McNally, the Lib Dem leader in the Lords, is normally regarded as a Kennedy loyalist, but yesterday he joined those expressing doubts.
"Charles has to recognise there is a good deal of discontent inside the parliamentary party about the style and content of his leadership since the general election," Lord McNally said live on BBC Radio Four.
"Charles has a lot to prove," he said. "The question is: is he given the chance to prove it or do we go into an election in January?"
The peer said Mr Kennedy at his best remained the ideal Lib Dem leader but conceded that since last May, the 44-year-old Highlander has been far from his best.
"Can he recover? He most certainly can but he has to recover by having good days followed by good days, followed by good days," Lord McNally said.
"He has got to give the party the sharper leadership which it clearly is asking for."
Despite winning another eight seats for a total of 62 MPs last year, Mr Kennedy faces internal criticism that most of those gains were won from Labour by emphasising the Lib Dems' opposition to the war in Iraq.
Many Lib Dem MPs believe those gains will be hard to hold at the next election, arguing that the leader should have given more time to winning over Tory voters.