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Amid a growing conviction that Mr Kennedy’s leadership was in its dying days, several more MPs told him that he must permanently resolve doubts over his lifestyle and self-discipline or go.
Others said that he had one final chance to rescue his position.
After an anguished day for the party, the view among senior Lib Dems was that they had no wish to humiliate the man who had led them to their best electoral position in modern times or to be seen to be panicking at the arrival of David Cameron as Tory leader.
But in private they bluntly told Mr Kennedy that his position was untenable as he spent much of the day in one-to-one meetings with Shadow Cabinet members.
He later met more junior MPs individually and spoke to others by telephone.
Parallel meetings went on between Lib Dem MPs and Andrew Stunell, the Chief Whip, in a move forced on Mr Kennedy by members of his Shadow Cabinet a day earlier to bring the issue of his leadership to a head.
In an interview on BBC One last night Mr Kennedy refused to say whether Menzies Campbell, his deputy, was backing him. On the third time he was asked Mr Kennedy replied: “They will take their decisions the next time an elected post comes around.”
Some MPs loyal to the Lib Dem leader staged a fightback as one, Lembit Opik, accused his critics of lacking the courage to state their concerns in public or even to Mr Kennedy in person.
Many more junior and recently elected Lib Dem MPs also rallied behind Mr Kennedy, expressing astonishment at the events of the past 36 hours and insisting that he remained a big electoral asset.
But their anger and surprise reflected the unusual nature of the crisis, which blew up in a closed meeting of the Shadow Cabinet and came after private discussions among more experienced MPs no longer prepared to tolerate his inconsistent performances or to give him another chance.
One senior MP, who told him that he could not recover, said: “I know half a dozen colleagues have said the same thing. Some people have said to him it is his last chance; some people are saying to him he has got to go.” Another, with an impeccable record of loyalty, said: “The current situation is unsustainable and has got to be resolved.”
Two who spoke to The Times indicated they believed that he would now have to resign. They thought the timing uncertain but were adamant that, if he were to go, it must be by the beginning of the year with no delay until the spring conference at Harrogate or later.
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