The gloomy prognosis is revealed in a survey of 2,000 adults published by the Social Market Foundation. More than three-quarters of those questioned feel the NHS has too little money and that, despite this, the demands on it are increasing.
There is a division of view about how it will cope with these pressures.
Three out of four think treatments will be rationed and two thirds believe the NHS will provide fewer treatments in 10 years than it does today.
On the other hand, more than half believe key services such as ambulances, outpatient visits and intensive care will have to be paid for.
Opposition to charging remains widespread, however, with more than half saying they would prefer tax increases to fund the service.
The survey was conducted in late July after the Government had announced the extra pounds 1.2bn for the NHS next year but before it had added the additional pounds 300m to get hospitals through the winter this year. The findings show how much Frank Dobson, the Secretary of State for Health, and his ministerial colleagues still have to do to rebuild public confidence in the NHS.
Professor Nick Bosanquet and Stephen Pollard say in "Ready for Treatment", a report on the survey, that the findings reveal an expectations gap between what the public would like the NHS to provide and what they believe it will be capable of delivering.
They add their voices to the growing number calling for the imposition of patient charges.
They say these should be set at a level similar to those already paid for other services: "If a prescription costs pounds 5.75, paying pounds 5 for a visit to the GP is hardly extortionate."