Nick Clegg told business leaders that such measures would ensure the economy was more resilient to future crashes.
Aides to the Liberal Democrat leader confirmed that the plan would take around 10 to 20 years, depending on what percentage of debt was cut.
In a keynote speech in the City of London, Mr Clegg warned that even once the UK closed its Budget deficit it would still owe £1.5 trillion - almost 80% of Gross Domestic Product (GDP).
A key LibDem priority in a Coalition government after the next general election would be to cut that debt to "sensible levels", he said.
He also accused Labour of failing to face up to the problem, saying the party had a "reckless" commitment to borrowing more money, threatening the economic recovery.
However, the LibDems last night said that, despite the sharp language, the party was not ruling out a future coalition with Labour.
Mr Clegg also attacked the Conservative Chancellor George Osborne's plans for £12 billion of extra welfare cuts after the 2015 general election.
He said the Tories had "ruled out asking the very wealthy to pay just a bit more in tax" in favour of hammering the working poor.
Despite the tough words on debt, the LibDem leader also suggested taxpayers should also be able to share in the proceeds of economic growth.
He said that the size of the state should grow as GDP - a proxy for a country's wealth - rises.
The LibDems want to stick to the Coalition's plans to balance the books and eliminate the structural deficit by 2017-18. That would still leave the UK's debt to GDP ratio at around 80%.
Mr Clegg said: "If we leave today's debts as they are, those future pressures will be unbearable.
"And, if we hand over high levels of indebtedness to our children and grandchildren, all we will do is leave them more vulnerable to inevitable future shocks."
Aides stopped short of saying that the same applied to personal and household debt.
Mr Clegg also criticised shadow chancellor Ed Balls's recent announcement that Labour would not balance the books until the end of the next parliament, in 2020.
The Liberal Democrat leader said that this approach showed that Labour had failed to learn the lessons of the financial crash.
He said: "Borrowing more, piling on more debt, diminishing the confidence of our creditors.
"It's reckless and it threatens the stability that's been achieved.
"Ed Miliband keeps promising a recovery for all, but there will be no recovery at all if you won't see through the difficult decisions and get the job done."