Health Secretary Andrew Lansley should "move on" from his role after NHS reforms in England are completed, Lib Dem deputy leader Simon Hughes says.
The prime minister has backed Mr Lansley, amid reports three Tory ministers privately attacked his handling of the issue.
Mr Hughes said the Bill would be better after changes made in the Lords, but still not what "we would have wanted".
Labour says the PM has put "political pride" before the NHS's best interests.
The Health and Social Care Bill aims to overhaul the way the NHS in England works, giving GPs more control of the NHS budget and boost the private sector's role.
Bodies such as the British Medical Association and Royal College of Nursing remain opposed to the reforms, despite concessions from ministers.
While giving GPs a bigger say has been welcomed by some, the competition element remains deeply controversial.
Mr Hughes, a senior Lib Dem who remains outside government, said amendments demanded by the House of Lords could get the bill "in better shape".
But it was still "not the Bill we would have wanted", he said.
Asked about Mr Lansley's position, Mr Hughes told BBC1's Andrew Marr show it might be for the best if he changed roles - but only after the reforms were in place.
"My political judgment is that in the second half of the parliament it would be better to move on," he said.
Shadow health secretary Andy Burnham vowed to give Mr Cameron the "fight of his life" unless he toned down the bill.
"Mr Cameron is making a grave mistake by saying he is going to force it on to the statute book," he told the BBC's Andrew Marr show.
Mr Burnham said he believed the bill - said to be proposing the biggest shake-up since the founding of the NHS in 1948 - would not be passed.
He said he was not against change but that the "back-room reforms" were a distraction from what the health service needed.
"We've argued all along that the government made a catastrophic mistake when it combined the biggest financial challenge in the history of the NHS with the biggest ever reorganisation."
His comments came after Mr Cameron accused Labour of opportunism over the issue.
The prime minister also said he "was at one" with his health secretary and there was no alternative to the changes going through Parliament.
"Choice, competition and transparency may unsettle some people," he wrote in a comment piece in the Sunday Times.
"But it's these things at the heart of our reform that will lead to the better NHS I care about and our country deserves."
His intervention followed the report of three of his party's cabinet ministers criticising Mr Lansley's handing of the bill, which applies to England.
And writing in the Mail on Sunday, Conservative backbencher Nadine Dorries also criticised the prime minister's approach.
"It is clear that Cameron wants to kill his own NHS bill - and Lansley's career with it."
But Communities Secretary Eric Pickles told BBC1's Sunday Politics: "I am not aware of any cabinet minister that has expressed reservations about the reforms."
Mr Pickles dismissed backbenchers' concerns that the reforms could cost the Conservatives a majority at the next general election, saying the party must "do the right thing".
And Culture Secretary Jeremy Hunt supported Mr Lansley, saying he believed he would eventually be seen "as the architect of the modern NHS".
Mr Hunt told the BBC Mr Lansley was the right person for the job and that it was wrong to judge someone who was "in the eye of the storm".