They have joined dozens of party members adding their names to an online letter urging the Deputy Prime Minister to step aside.
Clegg insisted on Friday that he would not quit despite more than 250 of the party's councillors losing their seats in local elections in England.
But with even the party leader conceding it is at risk of losing every one of its 11 MEPs when European election results are declared tonight, he is under pressure to sacrifice himself.
MP 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.
Jackie Porter, who is set to fight the Tory-held target seat of Winchester in next May's general election, said the party was "not going forward with a clear strategy".
The county councillor said the party's achievements were overshadowed because Clegg "allowed himself to be portrayed as just another pea out of the same pod" as David Cameron and Ed Miliband.
In order to win back support, the party needed to demonstrate it was different, she suggested.
She declined to say who she would like to see take Clegg's place.
Ms Porter is one of more than 500 to have signed up to the online LibDems4Change campaign which has published an open letter to Clegg.
It says voters have delivered a "stark message about the party's performance and direction".
"We consider it vital that at the 2015 General Election the Party should be led by someone who will receive a fair hearing about our achievements and ambitions for the future," it says.
"It is clear to us that this person is not you, as the loss of so many of our hard-working councillors highlights
"You have fulfilled a range of objectives in Government, but we now believe that progress will be best achieved under a new leader.
"We therefore ask that you stand down, allowing the membership to select your successor this summer."
Under existing rules, if Clegg refuses to quit, a leadership contest would be triggered if 75 local party associations formally demand one or a majority of the parliamentary party approves a no confidence motion.
Ros Kayes, the candidate in West Dorset, is another to have put her name to the letter.
In Thursday's elections, the Tories took charge of Kingston Council - the back yard of Energy Secretary Ed Davey - and the Lib Dems lost control in Portsmouth following gains by Ukip.
As the scale of the losses became clear, Clegg said he would "absolutely not" resign, and insisted the Lib Dems were still succeeding where they focused on their achievements in coalition.
He blamed a wider "anti-politics mood" but his party has seen its opinion poll ratings at consistently low levels since joining the Conservative-led coalition.
Clegg has said it is "flamingly obvious" that being part of the Government had damaged the party's chances.
Pugh told The Independent on Sunday that the party was to hold a "root-and-branch look at our current strategy, including how and by whom it is presented".
"I canvassed a number of backbench colleagues in the run-up to the elections and two very strong themes emerged.
"There was a widespread view that no matter how much Nick spoke there was a section of the electorate that would not give him a fair hearing.
"But equally, there was a need to avoid any civil war in the party."
He said the party appeared to have moved from an aggressive footing to a "less sustainable and more negative approach of digging in in our constituency trenches".
"We need to try to improve the national profile and try not to make Nick such an obvious target. It's the elephant in the room and the party can't ignore it."
A Liberal Democrat spokesman played down the significance of a review being carried out in the coming days - insisting it was standard practice to take stock after elections.
Another MP, John Hemming, said he would consider "whether any action is needed" when Parliament returned on June 4 and said he was "not an enthusiastic fan of Nick's leadership".