President Reagan has long been a supporter of "catastrophic" medical insurance to protect the individual against devastating costs from a long spell of illness or intensive care.

The idea is enormously appealing. A few months in hospital can run up bills of $100,000 or more, bankrupting even well-to-do families.

Under catastrophic insurance, for a relatively small annual premium, the individual is assured that once out-of-pocket costs exceed some fixed amount in a year -- say $2,500 or $5,000 -- the insurance will pick up all the rest. The premium is small because few people get that sick.

Reagan liked the idea so much that in 1972 he proposed it as governor of California, using a private-sector approach rather than making it a state program: all employers were to include in their on-the-job health insurance plans for their workers a catastrophic-protection feature.

"We found that if everyone who worked for a living in California paid $35 a year, they could be protected at limitless cost for life," he said last week. Three years ago he proposed a catastrophic-illness feature for Medicare.

In both cases he was unsuccessful. And previous congressional efforts to write catastrophic insurance into law have become entangled in disputes over who should pay for it, who should run it and how to provide it to low-income people who do not have any on-the-job basic health insurance.

But Reagan wants to try again.

In his State of the Union message Feb. 4, he ordered Secretary of Health and Human Services Otis R. Bowen to conduct a one-year study of how government and the private sector can provide catastrophic medical insurance, not just for the 30 million people on Medicare, but also for the general population.

The president's call for a one-year study appears to postpone any quick action on a Bowen plan for the government to provide catastrophic coverage to all Medicare beneficiaries and finance it through a $12-a-month increase in the $15.50 Medicare premium. On the other hand, the study opens the possibility of coverage for the whole population.

Some observers interpreted Reagan's charge to Bowen as a signal that the president will back a comprehensive national catastrophic-illness plan run by the federal government and financed through some form of federal tax -- like the current Social Security and Medicare systems.

But that is a misreading. "That's about the last thing we hope will come out of this study," said one official. And Tom Burke, Bowen's chief of staff, said at a public budget briefing, "I'm sure there's no intention to make this into national health insurance."

Rather, White House aides said, for the non-Medicare working population, at least, Reagan is almost certainly thinking of some form of what he proposed in California -- a simple catastrophic insurance add-on to private on-the-job health insurance policies, handled through the employer and the insurance company.

The cost of adding catastrophic-illness insurance to existing basic health policies would be relatively small, at least for hospital and medical care.

That is because few people spend much time in a hospital.

According to the American Hospital Association, the average hospital stay was only about 5.5 days in 1985 for people under 65. And for the Medicare population, which is older and sicker, the estimated average stay in 1984 was only 9.1 days.

Under Medicare, the patient pays $492 for the first day in hospital and then gets 59 days free in each spell of illness before further payment is required. HHS estimated that in 1982, only about 170,000 of Medicare's 27 million enrollees stayed more than 60 consecutive days.

Moreover, Pamela J. Farley of the HHS National Center for Health Services Research has estimated that in 1984, 50 to 60 percent of the population already had insurance providing substantial catastrophic protection -- mostly through job-based health policies. Normally, these policies limited out-of-pocket costs to between $750 and $5,000 a year. But most such clauses placed a limit on how much the insurer would pay over the beneficiary's lifetime -- usually $250,000.

That still leaves half the population uncovered, however.

The problem will probably be divided into three parts -- what to do about the Medicare population, what to do about everyone else for costs of acute illness, and what to do about long-term nursing home or home-health patients, a far more costly prospect.

Although only about 1.5 million elderly people are in nursing homes, the costs there are staggering -- $20,000 to $30,000 a year -- and are not covered by Medicare. Large numbers of people quickly use up their savings and have to depend on Medicaid, the charity medical program.

Aside from the nursing home issue, the big problem in providing catastrophic coverage for hospital and doctor bills is conflicts over the method of doing it. Reagan and other conservatives have been cool to the idea of handling catastrophic insurance as a government-run nationwide insurance program based on a government tax or fee.

Some insurance companies also were said to be unhappy with Bowen's idea of providing catastrophic coverage to the Medicare population simply by raising the monthly premium enrollees now pay the government, particularly as the new catastrophic benefits to be provided under the Bowen plan would replace privately sold "Medigap" policies that now provide such benefits.

Also, there is the problem of about 35 million people who have no health insurance at all, and of others with coverage that does not provide good basic protection, let alone catastrophic protection. Many of these people are poor, disabled or old and do not have jobs. Catastrophic coverage would take care of many middle-class people who have basic health insurance, but it won't do much for this 35 million.

Democrats have always insisted that providing basic health insurance for the normal range of illnesses for these left-out people should have a higher priority than catastrophic insurance, or at least the two should be linked. They fear that passing catastrophic coverage by itself would cause middle-class voters to lose interest in further health legislation to help the poor.