FOR THE FIRST time, the Medicare program faces sizable cutbacks in the health coverage it provides to Social Security recipients. As the Senate Finance Committee began last week to fulfill its obligations under the budget resolution, it voted to curb Medicare benefit growth by $13.6 billion over the next three years and to alter substantially the way that government does business with hospitals.

Medicare cuts tread on the interests of two powerful groups -- the elderly and the health industry. This consideration prompted President Reagan to put Medicare more or less off-bounds in his budget cuts last year. But there is no way for Congress to deliver the large cuts in domestic programs called for by the Reagan program without taking on the middle-class entitlement programs that dominate the domestic budget.

Although the Medicare cuts are the largest planned for any social program in the budget resolution, they are not large when compared with the size of the Medicare program itself. Next to Social Security, Medicare is the largest and fastest growing domestic program. This year it will spend almost $50 billion; over the next three years about $185 billion.

To control that growth, the committee would shift some costs to consumers and to health care providers. The amount of medical expenses that Social Security recipients would have to pay for hospital costs before Medicare coverage kicks in would rise each year -- from the current $75 -- along with the cost-of-living index. Premiums for doctor bill coverage would also rise slightly more than under current law. But as long as cash Social Security benefits also rise -- and as long as Medicaid coverage for the very poor is not eroded -- this is not an unreasonable requirement.

The loudest complaints are likely to come from the hospital industry. New controls would be placed on the ancillary services that now greatly inflate hospital bills. Medicare would also stop reimbursing hospitals for increases in daily costs that exceed 10 percent a year. In future years, this cap would be replaced by a system of fixed payments set in advance. The hospitals will claim that these controls will simply force them to shift unreimbursed costs to other patients. But private insurers are getting their backs up too and -- since gentler methods have failed -- it is time for the government to exert a little muscle to get hospital costs in line.

Government, primarily through Medicare, now purchases over half of all hospital care, and its reimbursement practices have contributed to the astronomical rise in hosital costs. Most of that increase was desirable -- health care for the elderly and the general population is far better than it was two decades ago. But if the country is serious about keeping medical costs from claiming an even larger share of national income -- both public and private -- it must begin now to accept some modest controls on their growth.