In a day of high drama for the LibDems, the peer, Lord Oakeshott, also appeared to implicate his close friend Vince Cable in a plot to oust Mr Clegg.
And he accused the party of corruption by offering places in the House of Lords in return for donations in a statement announcing his shock resignation.
Sources close to the LibDem leader last night insisted they did not think Mr Cable was involved in the attempted coup.
But the Business Secretary was later forced to go on television to deny he had known about Lord Oakeshott's actions.
The row came amid increasing pressure on Mr Clegg.
The local LibDem party in Cambridge has announced plans for an emergency meeting on his position. If enough local groups follow suit, they can potentially trigger a leadership election.
Critics of Mr Clegg believe that while this route is unlikely to be successful, the "drip, drip" effect could convince him to quit.
A close ally of Mr Clegg, LibDem peer Baroness Williams, revealed earlier this week that he had considered standing down in the wake of last week's local and European elections but had been persuaded to stay on.
Yesterday, in a series of parting shots that appeared designed to destabilise the party leadership, Lord Oakeshott hit out at the "disastrous" Mr Clegg.
Just hours earlier the peer had been told he faced disciplinary action after it emerged he secretly commissioned and published four other polls on key LibDem seats.
In his resignation statement, he warned the party the lesson of last week's council and European elections was "crystal clear" that it had to change its leader.
He praised those trying to force a leadership election, saying: "I have tried to give them the evidence they need to make the change. "I pray that they win, and that the right man, or preferably woman, is now elected to save the party."
He added that "my efforts to expose and end cash for peerages in all parties, including our own, and help get the Lords elected, have failed." He said he had told Mr Cable of the polls weeks ago, but said he was sorry to have "upset and embarrassed" the veteran LibDem.
The poll in Mr Alexander's political backyard of Inverness, Nairn, Badenoch & Strathspey puts him in third place behind the SNP and Labour.
The Chief Secretary to the Treasury received the backing of 16% of constituents, compared with the SNP on 32% and Labour on 25%, according to the ICM poll.
Mr Alexander took the seat in 2010 election with 40% of the vote, compared to 18% for the SNP.
A spokesman for Mr Alexander attacked the poll, saying it did not bear scrutiny. He criticised the sample size and the fact those who took part were asked a question that did not mention either Mr Alexander's name or the name of the constituency.
"Recent research has shown that LibDem MPs receive an 11-point lift in such polls when people are specifically asked to think about their own constituency and their MP," he added.
SNP MP Angus Robertson, who holds the neighbouring Moray seat, said: "The European election results gave us an idea of how badly the Liberal Democrats are doing as they were swept off the electoral map of Scotland, but for their senior cheerleader in the Tory-led No campaign to be relegated to third place is another humiliation.
"The LibDems are tearing themselves apart and this poll will make Danny Alexander wince as support in his own constituency evaporates, with only a slightly higher vote than the Tories in fourth place."