Two would-be Lib Dem parliamentary candidates -- staring at a much-reduced prospect of winning a seat at next year's general election -- have put their names to an online letter, signed by more than 200 party members, calling for Clegg to step aside.
He insisted Friday he would not quit despite being down 307 seats to 427 in the English local authority seats voted for on Thursday, with two of the 161 councils still to declare.
Clegg has acknowledged they could lose all 11 of their MEPs.
A projected national share of the local councils vote suggested that in a Britain-wide election, the Liberals would have been fourth on 13 percent -- having taken 23 percent in the 2010 general election.
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The anti-EU, anti-mass immigration United Kingdom Independence Party is now the chief beneficiary of protest votes, while many of the Lib Dems' left-leaning voters are disgruntled at the current coalition with the Conservatives.
The letter calling on Clegg to quit credits him with taking the Liberals into government for the first time in almost 80 years, but said the electorate had delivered a "stark message" about the party's direction.
Lib Dem lawmaker John Pugh -- while falling short of calling on Clegg to go -- described the local election defeats as "abysmal" and said they were "mostly due to national unpopularity".
"The high command is in danger of seeming like generals at the Somme: repeatedly sending others over the top while being safely ensconced in Westminster and claiming the carnage is all somehow sadly inevitable," he told the BBC.
A leadership contest could be triggered if 75 local party associations formally demand one or a majority of the parliamentary party approves a no confidence motion.
A Lib Dem spokesman said: "Now is a time to get our message across, and shout what we're doing in government, and not get distorted by needless infighting.