Over the last few days the Lib Dems have lost 250 councillors and all but one of their MEPs. The punishment at the hands of voters came after Clegg took a gamble by taking on Nigel Farage directly and positioning the Lib Dems as the unambiguously pro-EU party.
John Pugh, the MP for Southport, said the results were "abysmal they are worrying they are undeserved". He told the BBC on Monday afternoon that the deputy prime minister should fall on his sword as voters were simply "not listening" to him.
"My preference would be for a Cable succession, but thats not up to me, that's up to what the polls tell us about what will make the Lib Dems popular and successful and progressive its also what the party wants," he said. "If we carry on as usual then we are like the generals at the Somme because these loses are horrendous."
Pugh was one of the first Lib Dem MPs to break cover after the local election results were announced on Friday to call for Clegg to resign.
Senior Lib Dems including party president Tim Farron and former leaders Paddy Ashdown and Sir Menzies Campbell have urged colleagues to avoid naval gazing and insisted that Clegg should remain leader.
Campbell told BBC Radio 4's Today programme: "I haven't come wearing a black tie and with a funereal voice. There's no doubt in my mind that Nick Clegg is the person with the courage and the resilience to take the party through to and during, and indeed after, the next general election."
And Farron praised Clegg for having had the "backbone" to stand up to Farage and Ukip. "Britain is a diverse country, it is a country where we stand up for civil liberties, it is a country where we recognise that our national interests are in being part of the European Union," he said.
Farage predicted that Clegg would be ousted before next year's general election. He told BBC Radio 4's Today programme: "Nick Clegg's position clearly is very vulnerable indeed. I'd be very surprised if he led the Lib Dems into the next election. They have gone down to one seat and they've been beaten by the Greens in a national election, so I don't think the Lib Dems will stick with that."