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.
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."
Ed Balls said Osborne's comments were the "cynical act of a desperate chancellor". He said the UK needed to have a proper debate about welfare reform to ensure people cannot "languish on the dole for years and years on end".
"Our main thought at this time should be about the six children who tragically lost their lives, and the others in the family who have been left to mourn their loss," he said.
"And we should discuss what action needs to be taken to tackle the scourge of long-term unemployment including the need for a compulsory jobs guarantee so that people cannot languish on the dole for years and years on end.
"But for the chancellor to link this wider debate to this shocking crime is nasty and divisive and demeans his office."
Former Lib Dem education minister Sarah Teather has also sharply criticised the chancellor.
"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," she said on Thursday.
"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."