He claimed doing so would give a "pay rise of up to £6,000 a year" for more than seven million people.
He referred to a Channel 4 television documentary, aired earlier this week, in which a family struggling to make ends meet shared their daily experiences living in poverty.
How would the savings pledged by Labour be achieved?
In Wednesday's speech, the shadow chancellor repeated his party's commitment to bring the UK's energy providers into state ownership, a commitment he said would save the average UK household "an average of £142 a year".
A scheme of retrofitting homes with more efficient energy supplies would "slash the average household bill by over £400 a year".
He went on to say free childcare would provide a "saving on average almost £3,000 a year per child", whilst free school meals for all primary school children could cut household bills by £400.
Health and social care pledges from the Labour Party "for the personal care that we or our family members might need in old age" could mean a saving "of over £7,000 a year".
How realistic are the proposals by Labour?
It said among Labour's pledges, including compensating more than three million women who lost out when the retirement age rose, are "unfunded and uncosted".
Asked whether his pledge of £6,700 for families is any more real than Santa Claus, Mr McDonnell told ITV News Political Correspondent Libby Wiener: "None of this is rocket science, its basic common sense economics".
He went on to add an economy "that works for everyone" is "not about Father Christmas or make-believe. It’s about hard-nosed policy making."