They say that they won't cut Social Security this year, but both parties are moving to make cuts in its companion program, Medicare, which is also financed out of the Social Security tax and pays health care costs for 29 million aged and disabled people.

Medicare now is a $50 billion program, which pays more than a third of the nation's hospital bills. Some of the proposed cuts would drastically alter the way the government pays hospitals, and so perhaps the way hospitals themselves do business.

By far the biggest cuts, $23.3 billion over the next three years, are being proposed by the Republican leadership in the so-called Michel-Latta budget resolution now on the House floor, the budget alternative there that President Reagan is backing.

That is why House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) is accusing the Republicans of coming at the elderly, not frontally through Social Security, but by the back door through Medicare.

In contrast to Michel-Latta, the president's initial proposal this year called for $17.7 billion in Medicare cuts over the same period, the Senate budget resolution approved last week calls for $18.2 billion and the House Budget Committee's plan calls for only $9.4 billion.

Michel-Latta would add well over $2 billion in three years to out-of-pocket costs paid by Medicare beneficiaries. Most of the other proposals before the House add some out-of-pocket costs, too, but not nearly as much.

The added out-of-pocket payments would take the form of higher premiums for the doctor-insurance part of Medicare (an added $1.7 billion over three years), institution of payments for home health visits, and higher payments for doctor bills before Medicare kicks in ($100 million for these two items the first year), and postponement of Medicare payments until the first full month of eligibility ($545 million over three years). Of these four items, only the first-full-month proposal is in the House Budget Committee bill, which therefore adds only $545 million to beneficiaries' direct costs over the three-year period.

The Michel-Latta plan also would require a new system for paying hospitals. Now they are paid their costs for treating Medicare patients plus an added margin for return on capital; critics says this "cost-plus" system provides no incentives to hold down cost increases.

Michel-Latta is proposing a prospective reimbursement system, in which the amount the government would pay per patient would be fixed in advance and the hospital's payment from the government could not escalate beyond the fixed amount. Over half the entire $23.3 billion three-year saving is projected to come from this provision.

An alternative provision, also said to be under consideration as a way of achieving the saving, would limit reimbursements for "ancillary costs" in a hospital (costs beyond room and board, such as laboratory, radiology and special-room fees that generally are half a patient's hospital bill).

Medicare has long been a target of budget cutters because of its rapid growth, caused by escalating hospital costs. The cost per day of a hospital stay is rising about 16 percent a year, roughly twice the rate of increase in the Consumer Price Index.

The Michel-Latta proposal and the House Budget Committee measure share some features: both would require employers of people working past 65 to continue full private health insurance coverage for them and make Medicare the secondary source of payment.

The House Budget Committee bill also calls for some form of cost control over hospitals but estimates only $3.4 billion in savings from 1983 to 1985, about one-third Michel-Latta's $12.2 billion for this item.