Paying off the "NHS mortgage" is putting so much pressure on the system in England that the future of some hospitals is at risk, ministers say.
The government said 22 trusts - running 60 units - are facing difficulties because of the cost of paying for privately-funded building projects.
The group represents nearly a fifth of the 100-plus PFI schemes in the NHS.
Problems are being encountered because, for some trusts, repayments account for up to a fifth of their budget.
PFI is a way of funding building projects using private money. It was originally introduced by the Tories under John Major, but the use of the scheme was largely expanded into the NHS by Labour.
Under the schemes set up in the health service, private firms pay to build hospitals, leaving the NHS to pay an annual fee or "mortgage" over 30 years or so.
Department of Health figures show yearly bills are forecast to rise by 75% to more than £2.5bn in the next 18 years, because of inflation and the way the deals are structured.
It means once the last scheme signed off by Labour is paid in full - in 2049 - more than £70bn will have been handed over.
That figure also includes, in some cases, fees for services such as building maintenance, cleaning, catering and portering.
But even taking those services into account the sum far exceeds the value of the building projects, which stands at a combined £11.4bn.
Health Secretary Andrew Lansley said: "The truth is that some hospitals have been landed with PFI deals they simply cannot afford.
"Like the economy, Labour has brought some parts of the NHS to the brink of financial collapse."
But a Labour Party spokesman defended the deals, saying investment was needed "to replace the crumbling and unsafe buildings left behind after years of Tory neglect".
Health analysts have also said conventional hospital building projects could take decades to complete.
The Department of Health has said it will set out more details about its plans to resolve the problem later this year.
But sources close to Mr Lansley said if a solution was not found, money would have to be taken from elsewhere in the health service to "prop up" PFI hospitals.
There is a belief within some government circles that repayments could be reduced.
Professor John Appleby, chief economist at the King's Fund think-tank, believes renegotiation of the deals should be tried.
But he warned the NHS was not in a strong position because lenders feel confident the treasury will bail out trusts that get into financial difficulty.
"When these deals were negotiated there was more money flowing through the system and the NHS was probably a bit too optimistic about the future," he said.
"Money is getting tighter now and there is a drive to keep patients out of hospital. It is causing problems."
Some trusts named by the Department of Health rejected the suggestion their future was at risk, while others argued if NHS funding kept pace with inflation they could meet the repayments.
Concern was also expressed that the reorganisation of the health service was complicating matters.
David Stout, of the NHS Confederation, which represents health managers, said: "We do need to look at how we remunerate hospitals for their care, and if a hospital has high costs the government I think is right, and we would support this, the government does need to look at how we ensure they get the right amount of money to run that care.
"We don't want the care to be closed simply because of the cost of PFI, that would be foolish."
- The 22 NHS trusts that the government believes are at risk because of PFI are: St Helens and Knowsley; South London Healthcare; University Hospitals Coventry and Warwickshire; Wye Valley; Barking, Havering and Redbridge; Worcester; Oxford Radcliffe/Nuffield Orthopaedic Centre; Barts and the London; University Hospitals of North Staffordshire; Dartford and Gravesham; North Cumbria; Portsmouth; Buckinghamshire; West Middlesex; Mid Yorkshire; Walsall; North Middlesex; North Bristol; Mid Essex; Maidstone and Tunbridge Wells; Sandwell and West Birmingham; (not yet fully signed off) and the Royal National Orthopaedic Hospital (not yet fully signed off).