Working families often feel "exasperation" when they see other parents bringing up large families on benefits, the deputy leader of the Labour party, Harriet Harman, has said.

In a toughening of Labour rhetoric as the party draws up plans to return to the contributary principles of Beveridge, Harman said she understood people's resentment over high benefits while the economy stagnates.

Harman's remarks came as William Hague backed George Osborne's "absolutely correct" comment that the conviction of Mick Philpott had highlighted the need for a debate about Britain's welfare system. Philpott, who lived on benefits, was jailed last week for killing six of his children in a house fire in Derby.

Speaking on the BBC's Andrew Marr Show, Harman said: "It is absolutely understandable – when people limit their families to one or two children and feel they'd like to have a third but they can't afford it – the exasperation that people feel for the very small number of very large families that there are. But if you think of the Philpott family example, above all that was a problem of somebody who was just a criminal, a controlling person who was abusing everyone in their family as well as abusing the system. Fraud should be clamped down on."

But the Labour deputy leader, who served as social security secretary in the first year of Tony Blair's government, rejected a Tory idea to limit benefits after the second child. Asked whether the state should always provide support, regardless of the number of children in a family, Harman said: "I don't think that the state should be dictating family size. But I do think the state should support children."

Asked whether it had been fine for the state to support Philpott's 17 children, Harman said: "I don't think it is fine. I don't think anybody thinks what was going on in that family was acceptable, [particularly with] the violence."

Liam Byrne, the shadow work and pensions secretary, has outlined plans to toughen Labour's approach to welfare. In an Observer article, Byrne called for a return to the "old principle of contribution", pioneered by William Beveridge after the second world war, in which benefits would vary according to past contributions.

Harman said Byrne's proposals had three principles: work should pay, there should be an obligation to take work, and there should be support through a "contributary principle" for people who put into the system as well as those who take out.

This follows Labour's proposal for a job guarantee in which people over the age of 24 who have been unemployed for two years, and people under 24 unemployed for a year, will lose their benefits if they do not take a job when one is offered.

A new poll in the Sun shows that 67% of people believe the welfare system does not work and needs urgent reform. Harman said: "It is not surprising that people feel very concerned about the situation. You have got a twin problem: you have got an economy which is stagnating and so not generating jobs, and you also don't have a proper work programme so that people can be offered a job and if they don't take it their benefits are docked.

"The difficulty is for people who are in work seeing their standard of living pressurised – understandably they feel very resentful for people who are not working. For people who are looking for a job and can't find work it is deeply frustrating. For the small minority who don't want to work they are let off the hook by the fact there isn't a proper work programme."