A poll of 1,000 adult patients from England and Wales found that 54.4% agree that taxes have to increase to ensure long-term healthcare needs are met.
Around one in six (16.4%) are not confident that the NHS would be able to meet their needs in the future.
One in 10 patients believe they will have to pay for their healthcare in the future, according to the survey, conducted on behalf of accountancy firm KPMG.
Andrew Hine, UK head of health at the firm, said: "Few, if any, societies have truly faced up to the magnitude of the crisis of long-term care. All too often the debate over finance seems to overshadow the scale and gravity of the wider challenge which is, and always should be, delivery of quality care for patients.
"The onus is on a wide group of leaders to come up with an affordable way to pay for the care today's society will need, tomorrow. It's encouraging to see a heavy dose of realism, with many patients accepting that the Government can't be expected to cover all costs unless taxes rise substantially or major savings are made elsewhere."
An ageing population, more and more people suffering from long-term conditions and a stagnant budget are compounding factors putting pressure of the system, NHS England said.
If the health service in England continues to provide care the way it currently does, there will be a funding gap of £30 billion between 2013 and 2021, even if the health budget is ringfenced, officials said.
So to maintain a health service that is "free at the point of use", a new approach to providing services is "urgently needed", they said.