One poll in The Sunday Times put the party's support at just nine per cent and another for the News of the World found 46 per cent of those who previously voted for the party said they were less likely to do so again since it reneged on its pre-election pledge to oppose tuition fee rises.
Labour leader Ed Miliband yesterday issued an appeal to disaffected Lib Dem MPs to work with him, as part of efforts to capitalise on disaffection in their ranks.
Treasury Secretary Danny Alexander said the "only way out" was to press ahead with the "right" policies.
He also dismissed speculation over a leadership challenge to Lib Dem leader Nick Clegg, insisting the coalition was "rock solid" and would last for a full five-year term, despite further polling evidence that the leader was trusted by a quarter of people questioned – compared to two-thirds before May's election.
"Nick Clegg's leadership has been strong and purposeful and it's taken the Lib Dems into government," he said. "There is a real sense of purpose about this coalition, it is going to last over the five years because we have a very strong and radical programme of policies to deliver.
"There were a number of Lib Dems unhappy about the fees issue but actually on the coalition itself the party is united."
Mr Alexander said the party had known "it was going to be tough".
"The only way out of this is to continue to deliver our policies to do the right things for the right reasons," he added.
"I think people will come back to the Lib Dems as they see us doing that."
Deputy leader Simon Hughes admitted that the party had been badly damaged by the tuition fees issue.
"That is of course true but we always knew that the most difficult time for our party once the coalition deal was done was this moment," he said. "There is considerable anger that we've got ourselves into this position.
"And my plea to people in the party and outside who might be concerned at the moment as to where we're going is stay with us, because progressives are needed more now than ever in the history of the party."
Asked how the party could recover, he added: "It recovers by coming forward with the distinctive and radical policies that we have always campaigned for.
It recovers by being strong on civil liberties; by delivering, as we have started to do, the getting rid of identity cards; the reduction of detention without trial introduced by Labour.
"It, above all, wins by making sure we keep on progressive tax changes."
Former Conservative Prime Minister Sir John Major said the coalition could last beyond the 2015 general election.
"We are two separate but distinct parties that have come together for a fixed period of time – maybe this Parliament, maybe longer, very possibly longer.
"We're four years short of the next general election and if at the end of this parliament, the mess that was left to the coalition has been cleared up, a large part of the credit for that will go to the Liberal Democrats as well as to the Conservative Party."
Shadow Business Secretary John Denham said many Lib Dems were deeply unhappy with their leaders' "broken promises".
"We recognise there are people in the Liberal Democrats who are dismayed by what Clegg and the ministers are doing, who are not happy with it, and we will be reaching out to them and their supporters on this issue and others in the months to come," he said.