David Cameron has backed Chancellor George Osborne after he suggested a link between the Mick Philpott case and the need for welfare reform.
The prime minister told the BBC that living on benefits should not be a "lifestyle choice".
Unemployed Philpott has been jailed for killing six of his children in a fire.
Senior Lib Dem Danny Alexander has rejected Mr Osborne's comments, saying the Philpott case should be treated as an "individual tragedy".
Philpott was convicted of manslaughter, along with his wife Mairead and friend Paul Mosley, over an arson revenge plot that went wrong last year.
Much of the coverage of the trial focused on the fact Philpott, his wife and his mistress had lived with him at the three-bedroom council house in Derby with 11 of their children.
He received more than £8,000 a year in child benefit, as well as the income support and wages paid to his wife and mistress, which went into his bank account.
Philpott was jailed for life on Thursday.
Asked about the case on a visit to Derby on the same day, Mr Osborne said there was "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".
His comments provoked a storm of criticism from Labour and Lib Dem MPs, who accused the chancellor of trying to make political capital out of an appalling crime.
Mr Osborne's second-in-command at the Treasury, Danny Alexander also appeared to distance himself from the chancellor's remarks.
The chief Treasury secretary said: "George Osborne is right that there needs to be a wide debate about the future of our welfare system, but the Philpott case is an individual tragedy.
"I think that's where we should let that case lie. I wouldn't want to connect that to the much wider need to reform our welfare system."
However, speaking on a visit in his constituency of Witney in Oxfordshire, Mr Cameron threw his weight behind Mr Osborne, saying the chancellor had made a point of stressing Philpott was "responsible" for his crimes.
"But what the chancellor went on to say is you should ask other questions about our welfare system," said Mr Cameron.
"We want to say welfare is there to help people who want to work hard, but it's not a lifestyle choice."
For Labour, shadow chancellor Ed Balls called Mr Osborne's remarks the "cynical act of a desperate chancellor", adding that "to link this wider debate to this shocking crime is nasty and divisive and demeans his office".
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.