Lib Dem leader Charles Kennedy has hit back at claims 3,300 party members - including 386 councillors - have signed a petition calling on him to quit.
Mr Kennedy vowed to continue as leader and said the Liberal magazine, which organised the online poll, had "nothing whatsoever to do with our party".
He said party headquarters had received many messages backing his leadership.
Liberal editor Ben Ramm said his poll reflected a growing mood in the party that Mr Kennedy should stand aside.
Describing a broad range of people who had backed the petition, he said: "We have grassroots activists, councillors, those within Cowley Street (Liberal Democrat HQ) itself.
"They come from across the country and seemingly from what would be called left and right."
He said he thought Mr Kennedy should "go immediately", adding "we must have a new leader by mid March for the spring conference".
He told the BBC News website Mr Kennedy was a "nice guy" but lacked a compelling vision and coherent strategy to take the party forward.
"The Liberal Democrats need to shape the debate rather than be shaped by it. Kennedy has been shaped by it," he added.
This year's general election, which saw the party elect 62 MPs, its highest total since the 1920s, was "a massive opportunity missed" to increase the party's strength at Westminster further, Mr Ramm added.
He said the election of David Cameron as Conservative leader had "focused the minds" of the party's new MPs, many of whom feared they would lose their seats at the next election.
He said there was a "serious possibility" the Lib Dems would be reduced to 29 seats at the next election if Mr Kennedy continued as leader.
Mr Ramm, who is on the Lib Dem candidates list for the next general election, said two MPs and 386 local councillors had signed the Liberal's petition on its Kennedy Must Go website.
He said he was confident the signatories were genuine but he could not release their names.
Mr Kennedy has made repeated attempts to reassert his authority since concerns about his leadership were raised at the party's annual conference in October.
Deputy leader Sir Menzies Campbell and party president Simon Hughes are widely thought to be the frontrunners to replace him.
One senior Lib Dem MP has reportedly threatened to hold a vote of no confidence if Mr Kennedy did not step down in the next 14 days.
But parliamentary party chairman Paul Holmes said calls for Mr Kennedy to step down were a "made-up story" and he had not been approached by anyone expressing doubts about Mr Kennedy's leadership.
Mr Kennedy has vowed to fight the next election as leader and says he has the full backing of his MPs.
Asked on BBC Radio 4's The World At One, why - according to the Liberal poll - one in 12 local councillors wanted him out, Mr Kennedy replied: "I would be very surprised if that were the case, let me put it no stronger than that, very surprised indeed.
"I don't think I should be paying, or the Liberal Democrats should be paying, any more attention to this than if it was coming from the Labour Party or the Conservatives as a criticism."
He said that 90% of messages which the Liberal Democrats had received on the subject were in support of him.
Mr Kennedy said he was not worried that the rumours about his future could destabilise him.
And he issued a challenge to any MPs who had been briefing that his position is unsustainable: "Well, if they feel that, let them come on The World At One and discuss it."
He was speaking after senior Liberal Democrat MP and former deputy leader Alan Beith said the New Year would provide an opportunity to consider whether Mr Kennedy was up to leading the party to the next general election.