A coalition rift was blown into the open when the Liberal Democrats condemned George Osborne for "playing politics" with the deaths of six children after the chancellor highlighted the Mick Philpott case to raise questions about high welfare payments.

Amid deep unease among senior Lib Dems – up to and including Nick Clegg – over the Conservatives' use of the deaths of six children to make the case for controversial welfare reforms, the party went out of its way to distance itself from the chancellor's remarks.

Danny Alexander, the Lib Dem chief secretary to the Treasury, who is usually careful not to criticise the chancellor, made clear his unease. "The Philpott case is an individual tragedy," he said. "Children have died in that case. I think that is where we should let that case lie. I would not want to connect that to the much wider need to reform our welfare system."

In the most hard hitting remarks by a Lib Dem, the party's former Treasury spokesman accused the chancellor of playing politics with the deaths. Lord Oakeshott of Seagrove Bay said: "You can forgive George Osborne's immaturity and inexperience as chancellor but not this calculating, callous cruelty. If he can't see it is wrong to play politics with the death of six children, he is not fit to be chancellor."

Oakeshott, who acts as an informal adviser to the business secretary Vince Cable, often does not reflect the thinking of the leadership. But Cable is understood to feel that vilifying people on benefits in the way Osborne has done is misplaced.

The Lib Dems spoke out after David Cameron strongly endorsed Osborne's decision to call for a debate on whether it was right to be "subsidising lifestyles like that" – a reference to the Philpott case. The prime minister told the BBC in his Witney constituency: "I think what George Osborne said was absolutely right. He said that Philpott was the one to blame for his crimes and he should be held responsible.

"But what the chancellor went on to say is that we should ask some wider questions about our welfare system, how much it costs and the signals it sends. And we do want to make clear that welfare is there to help people who work hard and should not be there as a sort of life choice. I think that is entirely legitimate."

Cameron's intervention shows that the Tories are prepared to use the case of Philpott, who was said to have been claiming £54,253 a year in benefits with his partners and children, to reinforce the series of welfare changes coming into place this month. These include a £26,000 cap on household benefit claims.

On Thursday, Philpott was given a life sentence for the killing of his children in a house fire in Derby. Mrs Justice Thirlwall said he should serve a minimum of 15 years in jail.

The chancellor sparked a storm of protest on Thursday when he questioned the way in which Philpott had been able to claim high levels of benefits. Speaking in Derby, the town where the killings took place, Osborne said: "Philpott is responsible for these absolutely horrendous crimes and these are crimes that have shocked the nation. The courts are responsible for sentencing him, but I think there is a question for government and for society about the welfare state – and the taxpayers who pay for the welfare state – subsidising lifestyles like that, and I think that debate needs to be had."

It is understood that the deputy prime minister believes that the arguments in favour of benefit reforms, introduced at great political expense to the Lib Dems, have not been helped by the interventions of the chancellor and the prime minster.

"It is not a parallel that would be drawn by any Liberal Democrat," one senior source said of the link between the Philpott case and the welfare shakeup. "There is an important debate that we are having in this country about welfare and how we continue to have a welfare system that meets the test set out by the great Liberal, William Beveridge, that supports people who need help but that is also affordable to the taxpayer. That debate is happening now in Britain and it is a healthy debate for a country to have. But it cannot be linked to individual cases no matter how horrific they are."

Frank Field, Labour's former welfare reform minister who is supportive of some of the government's welfare changes, was also critical of Osborne for penalising people whose lifestyles have been encouraged by the state. "My only caution to the government is this shows the attitude they had with the Child Support Agency [in the 1990s] where they thought you could just tear up a state of affairs which we politicians had allowed to occur.

"There is all the difference in the world [between] saying that if we make changes it will be for future families and penalising children now in families who have been given a nod and a wink for decades to behave as they want."

Field, who supports the benefit cap but is highly critical of the "bedroom tax", says the chancellor is being naive.

"Where has George Osborne been for heaven's sake? Has he never canvassed? That is why some of us have been serious about welfare reform – but not what they are doing now."

But he added: "By all means we should have a debate about it. But the idea we should then retrospectively impose these changes is wrong.

"We as politicians have allowed this state of affairs to develop. Where were we when this was all going on?"