In one of the boldest policy initiatives in his budget, President Reagan yesterday proposed to change the way the nation pays its medical bills.

The proposals constitute the administration's long-awaited plan to control medical inflation, under discussion for two years in the Cabinet and White House.

Through a combination of tax increases and reimbursement limits, the package would shift directly to patients, hospitals, doctors and other medical service providers a substantial portion of the cost of medical care now paid by private sector employers, insurance companies or the government.

One immediate impact would be to save money for the government on Medicare and Medicaid.

But the more important impact, the administration hopes, would be to make both users and providers of medical care more cost-conscious because money would be coming out of their pockets. The belief is that this heightened cost-consciousness, by curbing marginal demand for services and encouraging efficiency in providing them, would help hold down health-care costs, which rose 11 percent last year, compared with a 3.9 percent inflation rate for the economy as a whole.

The general concept has been known for some time, and many Democrats as well as organized labor leaders are extremely critical of it, arguing that the presumed benefits are speculative but the immediate costs are clear: less money for health care.

On the other hand, the basic structure of the plan has been endorsed by Chairman Robert J. Dole (R-Kan.) of the Senate Finance Committee, which has jurisdiction over most government health programs.

The keystone of the plan is a proposal to make employes pay federal income taxes on health insurance premiums paid by their employers to the extent that they exceed $840 a year for an individual or $2,100 per family. Now health insurance premiums financed by the employer are not counted as income and are not taxed, which, critics of the current system contend, encourages the creation of high-cost plans.

According to assistant Secretary of Health and Human Services Robert Rubin, the proposal would mean additional taxes for about 30 percent of the 160 million people who have employment-based health insurance. The proposal would bring in about $2.3 billion in added revenues in fiscal 1984, HHS estimated. Additional, smaller amounts would accrue to the Social Security system and to the states.

A second feature of the plan would apply similar economy concepts to Medicare, the $66 billion federal program that provides health benefits to 29 million aged or disabled Social Security recipients.

Under the president's proposal, Medicare patients would be required to pay more out of their own pockets for the first 60 days of hospitalization under Medicare. But once they had been in the hospital for 60 days, a "catastrophic" illness protection feature would kick in and the government would pay hospital costs for all additional days.

Here again the goal is increased cost-consciousness.

HHS said that the Medicare patient now pays a basic fee for the first day, which is estimated at about $350 in 1984, the first year the new system would be in effect. Then he pays nothing out of pocket for the next 59 days, $87.50 a day (again an estimate for 1984) for the 61st to 90th days, $175 a day (1984) from the 91st to the 150th day and the entire cost ($350 a day or more) for all days over 150.

HHS said the absence of any charge from the second to the 60th day "gives no incentive to the less ill to keep their hospital stays short," while the requirement that the patient pay everything after the 150th "penalizes the severely ill."

Under the president's plan, the patient would pay the initial $350 plus 8 percent a day ($28 a day) for the second to 15th day and about $17.50 a day from the 16th through 60th. After that, the government would pay all hospitalization costs.

HHS said that the patient who stayed in the hospital 15 days would pay $350 out of pocket under the current system and $742 under the president's plan, admittedly more. But in return for this higher charge for the initial days in hospital, if the same patient ended up staying 150 days, his out-of-pocket bill under current law would be $13,475, but under the proposal only $1,529 because of the "catstrophic" protection feature.

HHS said the average Medicare patient stays in the hospital 11.5 days, and only 170,000 to 200,000 experience a spell of illness exceeding 60 days. This proposal, already criticized by Sen. Edward M. Kennedy (D-Mass.) and Rep. Henry A. Waxman (D-Calif.) as making most people pay more, would save Medicare a net of $663 million in fiscal 1984 and $1.2 billion in fiscal 1985 because income from the added payments during the first 60 days would, overall, outweigh the costs of providing catastrophic coverage.

A third provision in the plan would create a system of prospective payments (based on types of illnesses) for government reimbursements to hospitals under Medicare. The amount to be paid would be fixed in advance, and hospitals thus would have an incentive to improve efficiency and monitor stays more closely to bring down costs.

A fourth feature of the plan would allow a Medicare beneficiary, if he chose, to opt out of Medicare and obtain a government voucher worth 95 percent of the per-person costs of the Medicare program, to buy private health insurance.

Other Medicare and Medicaid provisions were not classified formally as parts of the "cost-consciousness" package, but many would fit in with it by requiring patients to pay more and presumably encouraging them to think more carefully before demanding services.

Thus, the premium for Part B, the doctor-insurance part of Medicare, which usually rises slightly each year, would be frozen at the current $12.20 a month for the rest of 1983, but raised from its current level of about 25 percent of program costs to about 35 percent by 1988. The change would cost the government money the first year but boost its revenues by $9.3 billion from 1984 to 1988.

Another provision would increase annually, to keep pace with inflation in medical costs, the $75 a year that Medicare patients now must pay toward their doctor bills before Medicare benefits take effect.

Others would freeze rates of Medicare reimbursement for physicians for a year (saving $700 million); make Medicaid patients pay $1 or $1.50 for doctor visits and $1 to $2 for each day in hospital; reduce federal reimbursements to states under Medicaid by 3 percentage points per state compared with what they would have been under the law before Reagan became president, (continuing, with some changes, a 1981 Reagan proposal that Congress passed), and make several other Medicare changes reducing reimbursements to hospitals or making patients pay a greater share.

According to HHS, net Medicare-Medicaid outlays would be about $2 billion less in fiscal 1984 than under existing law; but the impact of many provisions would be greater later.