David Cameron has stepped up clashes with Labour by insisting the case of child killer Mick Philpott did raise "wider questions" about the welfare system.
The Prime Minister echoed comments by George Osborne, saying society had to consider what "signals" benefits sent.
However, the Chancellor's Liberal Democrat deputy Danny Alexander said he did not believe the case should be linked to the coalition's controversial shake-up.
Mr Cameron told reporters: "I think what George Osborne said was absolutely right. He said that Mr 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."
Philpott, who was jailed for life for killing six of his children in a fire, lived in a council house in Derby, claimed thousands of pounds in benefit and refused to get a job. He was handed a 15-year minimum term after being convicted of manslaughter along with his wife Mairead and friend Paul Mosley.
On a visit to Derby, Mr Osborne was asked if the Philpotts were a product of Britain's benefit system. "Philpott is responsible for these absolutely horrendous crimes, these are crimes that have shocked the nation. The courts are responsible for sentencing," he replied.
"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."
The remarks drew a furious response from shadow chancellor Ed Balls, who accused Mr Osborne of demeaning his office. "We should have a proper debate about welfare reform," he wrote on his blog. "But for the Chancellor to link this wider debate to this shocking crime is nasty and divisive and demeans his office."
Senior Lib Dems have been holding back from getting involved in the row but, when asked about the issue today, Mr Alexander replied: "The Philpott case is an individual tragedy. 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."