Nick Clegg is facing calls to quit as Liberal Democrat leader after his party's dismal showing in the local elections.
The Deputy Prime Minister's position has come under scrutiny after the Lib Dems lost more than 250 councillors in local elections - with the results of the European polls to be announced later on Sunday.
Southport MP John Pugh said up to 12 of his colleagues in the Commons have expressed doubts over Mr Clegg's position as leader, and called for a debate on "the leadership issue" within the party.
"Although I admire enormously Nick's bravery, it does not follow that because the captain should go down with the ship that the ship has to go down with the captain," he told the Sunday Times.
Colleague Adrian Sanders, who represents Torbay, added: "The problem is the messenger, very few people say it's the message."
But Lib Dem chairman Tim Farron told the BBC's Andrew Marr show: "I have lost elections before and it is miserable, and I also understand why these people will feel that the message that they got back on the doorstep, that they don't like us being in government and so on, is a really difficult one.
"But I just think, at this time, it would be absolutely foolish for us as a party to turn on ourselves."
The Lib Dems are privately accepting of the fact that they could lose all 11 of their MEPs when results are announced at 10pm tonight.
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, Mr 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.
Two would-be MPs are among more than 600 people who have signed up to the online LibDems4Change campaign which has published an open letter calling on Mr Clegg to step down.
