Ed Miliband has accused the government of setting back the chances of young people and said Labour must "stand up" for the hopes of the next generation.
The Labour leader said the coalition was endangering the "British promise" - the expectation that children will have more opportunities than their parents.
In a speech in Gateshead, he called for "more equality between generations".
The coalition argues that paying off the UK's debt is a "precondition" of future growth and prosperity.
Mr Miliband and deputy prime minister Nick Clegg both set out their visions for future economic growth and social mobility on Friday.
The Labour leader said the history of his own family - his grandparents settled in the UK after fleeing from Nazi-occupied Europe - was an example of what he described as the "British promise".
But the expectation that the next generation would be more prosperous and have greater chances than the last was "under threat like never before", he argued.
Spending cuts would make it harder for young people to stay in school after 16, to go to university and to be able to own their own home.
While the better-off in society would be able "to pass on privilege and wealth", he said middle and lower income groups would be disproportionately affected.
Though not doubting David Cameron or Nick Clegg's wish to leave the best possible legacy to the next generation, he questioned whether they understood the "sense of shared responsibility" needed to help everyone get on in life irrespective of their background.
It was up to Labour to defend this promise of inter-generational progress - which he compared to the American dream - in the face of the coalition's desire to cut the deficit as "far and fast" as possible.
"I want to do my bit to make sure that the promise of progress for the next generation can be passed on," he said.
He argued that policies such as nearly trebling the cap on student tuition fees in England and scrapping the educational maintenance allowance would "take away the ladders" for young people and have a profound impact on the country's future.
"You go from education maintenance allowance to what's happening to tuition fees, to apprenticeships, to child trust funds - to a whole range of things where the government is taking action setting back the chances of future generations."
'Burden of debt'
While the coalition was focused on short-term solutions, Mr Miliband said there was need for a more far-reaching national debate about how to ensure that "there is not just equality within a generation but between generations as well".
"I think our responsibility as a party... is to be the people who stand up for the next generation," he added. "I think that makes us the optimists in Britain today. We are the people who actually believe the next generation can be better than the last whatever the challenges they currently face."
Mr Miliband also announced a series of policy reviews focused on the family, housing, parental involvement in schools and opening up the creative industries to a wider cross-section of the public.
Higher Education minister David Willetts said Labour's legacy to the next generation was a mountain of debt which meant every child would owe the equivalent of £22,000 unless the government reduced levels of borrowing.
"Easing that burden of debt on future generations is one of the best ways that government can help them," he told BBC Radio 4's World at One programme.
The government had "a social mobility plan alongside the deficit reduction plan", he said, which would ensure more money would go to schools in the most deprived areas, students would not have to pay for university fees up front and thousands more apprenticeships would be created.
"At best social mobility stalled under Labour," he added. "That is essentially why we have to get on with the job of improving social mobility."