In their drive to hold down the deficit, President Reagan and some in Congress want to cut the government's largest health care program, Medicare for the aged and disabled, but 84 percent of the American public believe that Medicare should not be cut under any circumstances, according to a Washington Post-ABC News poll.

The poll, conducted in early March using a nationwide sample of 1,050 people of all ages, revealed opposition to Medicare cuts not just from the elderly but from the young. It illustrates one of the budget conundrums faced by Congress and the Reagan administration.

Aid to the elderly, primarily in the form of Social Security and Medicare, is now over one-quarter of the entire federal budget, but politically it is virtually uncuttable.

With 26 million people age 65 or over, the elderly constitute one of the biggest voting blocs in the nation, and nearly 70 percent of them actually do vote, according to Census Bureau figures; for the population as a whole only 59 percent do.

The opposition of the aged to cuts in programs affecting them was underscored yesterday when the Leadership Council of Aging Organizations, representing 18 million people, virtually declared war on Reagan's 1983 budget and on proposals to cut the next scheduled Social Security cost-of-living increase, declaring these would have a "devastating" impact on the elderly.

Last year a Reagan proposal to make significant cuts in Social Security provoked such hostililty that he had to abandon it and appoint a special commission to study Social Security's problems.

The new poll suggests Reagan may face similar political problems with his proposals this year to chop $3 billion from Medicare.

More than one-tenth of the entire federal budget now goes for health programs, and Medicare, with 29 million aged and disabled beneficiaries and estimated outlays of $58 billion in fiscal 1983 if there are no cuts, is the undisputed giant.

It is an enormously popular program because nearly everyone in the country either is entitled to benefits or will be and has elderly relatives who are.

Yet it is also a tempting target for budget-cutters. Medicare pays one-quarter of all the nation's hospital bills and 40 percent of all the medical bills of the aged. It is one of the fastest-growing federal programs, if not the single fastest-growing. Only 12 years ago it cost only $7.5 billion.

Arguing that the Medicare payment structure is too loose and may even encourage waste, overutilization and overpayment, Reagan has proposed $3 billion in Medicare cuts next year so that the program would increase only to $55 billion.

The Post-ABC News poll reveals very substantial opposition to the idea of further cuts in Medicare at all age levels.

In the poll, respondents were asked this question: "Which of the following statements comes closer to your own view?

"A. Under no circumstances should Medicare aid to the elderly be cut back.

"B. Because of the financial crunch, Medicare, like other government programs, should be cut back."

Overall, 84 percent chose statement A as reflecting their feelings, 13 percent chose statement B, and the rest gave no clear answer.

With some variations, the 84 percent opposition to cuts held true for all age groups.

The poll also revealed that 18 percent of all households contained someone getting Medicare, but the figure was much higher, about two-thirds, for aged households.

On another question, 65 percent said that even given all its expenses, the government doesn't spend as much as it should on the elderly.