ConservativeHome editor says health secretary has failed to win public support for health and social care bill.
One Tory minister said Lansley should be replaced, another compared his NHS reforms to the poll tax, ConservativeHome said.
David Cameron has been urged to replace Andrew Lansley and drop large chunks of the health bill by the Conservative party's most widely read and influential website.
Tim Montgomerie, the editor of ConservativeHome, said in a post published on Friday that Lansley, the health secretary, had failed to win public support for the legislation and that, if the Tories did not back down, every problem with the NHS over the next three years would be blamed on the bill.
The ConservativeHome intervention is particularly damaging to Cameron because Montgomerie says he was encouraged to speak out by three Conservative cabinet minsters who believe that pressing ahead with the bill would be folly.
"One was insistent the bill must be dropped. Another said Andrew Lansley must be replaced. Another likened the NHS reforms to the poll tax," says Montgomerie in his article.
"The consensus is that the prime minister needs an external shock to wake him to the scale of the problem."
ConservativeHome is not officially linked to the Conservative party.
But it is read by thousands of activists, whose views it broadly represents, and, although it does criticise government policy, it is generally supportive and not given to gratuitous attacks on the party leadership.
On Friday Montgomerie told the Today programme why he had decided to publish his article. "I wrote this blog this morning because I think the feeling is David Cameron isn't listening enough to internal party feeling and this is why I have gone public," he said.
As the Guardian reported on Thursday, Cameron and Nick Clegg have decided to press ahead with the bill, which is still in the House of Lords, even though it has become a political liability.
This week the Times quoted a Downing Street source saying Lansley should be "taken out and shot" because he was handling the issue so badly.
But Montgomerie argues that if the bill does become law, it will lead to the coalition being blamed for everything that goes wrong with the NHS between now and the election.
"The NHS has always gobbled up resources and creaked. The creaking was severe when spending was increasing by 3% or 4% in real terms every year," he writes.
"What do you think it's going to be like when spending is increasing by 0.1% year after year after year in this longest ever period of UK-wide austerity? The creaking could have been blamed on the empty Treasury and Labour's over-borrowing. Not now. It will now be unfairly blamed on the bill and a bill that is not only mangled and bureaucratic, but also unnecessary."
Montgomerie says Cameron faces a choice. "Path one involves removing all contentious components of the bill," he writes. A gutted bill could then be passed with cross-party agreement. "It would be humiliating to forge such a cross-party deal but the humiliation would subside over a few weeks.
"Path two involves pressing on. It's the path that, despite his rhetoric, Ed Miliband prays the coalition will tread.
Pressing on avoids the immediate political pain but leaves the chronic electoral problem in place. By 'succeeding' in enacting a contentious bill every inevitable problem that arises in the NHS in the years ahead will be blamed on it.
That's a heavy price to pay for a bill that is neither transformational nor necessary."
Montgomerie, who says that Cameron's "greatest political achievement" as leader of the opposition was to stop the Conservatives being seen as an anti-NHS party, says Lansley should go.
["He hasn't been able to communicate these reforms in a streetwise way," Montgomerie says.
Echoing a point repeatedly made by Stephen Dorrell, the former Conservative health secretary who now chairs the Commons health select committee, Montgomerie says that implementing structural NHS reform is perilous at a time when the NHS already has to find savings of £20bn.
Reacting to the ConservativeHome editorial, shadow health secretary Andy Burnham said: "We already know that the Prime Minister isn't listening to doctors and nurses.
[But it's a shock to find out that even senior members of his own Cabinet have to take to a Conservative website to get through to him about the damage he is doing to the NHS.
"It couldn't be clearer: this is an out-of-touch Prime Minister who is putting his political pride before the best interests of the NHS," he said.
"David Cameron promised to protect the NHS but every day he digs in behind his Bill, he damages it further."
The ConservativeHome broadside was published after it was revealed that Lib Dem activists want to call a vote on scrapping the bill at the Lib Dem spring conference next month.
The Lib Dem leadership managed to keep a second health rebellion off the agenda of the autumn conference, but will face intense grassroots pressure if it tries to prevent debate again.
An emergency motion can be kept off the floor of the conference if it is not deemed an emergency by the federal conference committee, or it is not selected for debate in a ballot of delegates.
In an effort to keep up the pressure on the coalition, Labour has agreed to hold an opposition day debate later this month demanding publication of the bill's risk register, a confidential government document setting out all the risks associated with the legislation.
Critics believe the risk register, which Lansley has repeatedly refused to publish, contains damning warnings about rising costs and confusion.
Concern has been heightened after it emerged on Wednesday that a risk assessment by the London NHS warned some organisations could fail financially and care,
including maternity and children's services and public health, could suffer. Such is the anger about the register that nine Liberal Democrats are already among 50 MPs who have signed an early day motion also calling for it to be published – and Labour believes more Lib Dems will support its move.
To put further pressure on the coalition, Andy Burnham, the shadow health secretary, will urge Labour MPs to visit hospitals and surgeries during next week's half-term break, so they can recount their stories from the NHS frontline in the debate on 22 February.
"The defining question in this debate now is, by pressing on and not listening, to what extent are they putting patient safety and quality of services at risk, and that's why the risk register becomes absolutely central to this," said Burnham.
Lansley faced fresh embarrassment on Friday when a report by the right-of-centre thinktank Reform said the government's entire reform of public services was being undermined by the Department of Health's management of NHS changes.