Chancellor George Osborne is at the centre of a political row after questioning whether the state should "subsidise" the lifestyles of people such as Mick Philpott.
Unemployed father-of-17 Philpott was jailed for life on Thursday for killing six of his children in a house fire.
Mr Osborne said there was a "question for government and society" about the influence of benefits on behaviour.
But Labour condemned the comments as "a cynical act of a desperate chancellor".
Philpott was convicted of manslaughter, along with his wife Mairead and friend Paul Mosley, over an arson revenge plot that went wrong.
Much of the coverage of the trial focused on Philpott's lifestyle and the fact that his wife and his mistress Lisa Willis had lived with him at the three-bedroom council house in Derby with 11 of their children until Miss Willis moved out in February 2012.
George Osborne has sent out the message that he thinks there is a link between Mick Philpott's lifestyle and the welfare debate.
Ed Balls has accused Osborne of playing politics with a human tragedy.
There are risks for both sides.
Voters may think the Conservatives are making political hay from a unique and horrific crime.
They may think Labour sounds insufficiently tough on welfare.
Or they may just think this is another round in a long fight between two big political beasts.
Philpott received more than £8,000 a year in child benefit for his 11 children, as well as the income support and wages paid to his wife and mistress, which went into his bank account.
He had already achieved tabloid notoriety as "Shameless Mick" and "Britain's biggest scrounger" before his trial began.
In 2006 he appeared on The Jeremy Kyle Show, on ITV, to demand a bigger council house.
Mr Osborne, who has been defending government cuts to housing benefit and other welfare changes, which came into force this week, 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."
But, in a blog post, Labour's shadow chancellor Ed Balls was highly critical of his opposite number, saying: "George Osborne's calculated decision to use the shocking and vile crimes of Mick Philpott to advance a political argument is the cynical act of a desperate chancellor."
Mr Balls demanded "a proper debate about welfare reform".
"But for the chancellor to link this wider debate to this shocking crime is nasty and divisive and demeans his office," he added.
Former Liberal Democrat education minister Sarah Teather joined in the criticism, saying she was "shocked and appalled that George Osborne has stooped so low as to make a crude political point out of the tragic deaths of six young children".
"It is deeply irresponsible for such a senior politician to seek to capitalise on public anger about this case, and in doing so demonise anybody who receives any kind of welfare support," the MP for Brent Central said.
"Mr Philpott should be held fully accountable for his awful actions and it is reprehensible to seek to explain it away by blaming the welfare system which Osborne has been so happy to wage war on."
But Conservative Party chairman Grant Shapps backed the chancellor.
He said: "I think we should be proud of having a welfare system that looks after the most vulnerable in our society. It's a proper safety net. Of course there a proper debate to be had about where this should begin and end, and of course that case highlighted some of the extremes."
Philpott has been told he will serve a minimum of 15 years in prison, while Mairead and Mosley were told they would serve at least half of their 17-year sentences.
During the trial, the prosecuting lawyer told the jury: "Michael Philpott did not want to work. He just wanted a house full of kids and the benefit money that brings."
Mr Osborne has dismissed claims that his benefit reforms mark the end of the welfare state as "shrill, headline-seeking nonsense", arguing instead that they encourage people to work rather than rely on payments.