President Carter, siding with his health and domestic advisers, is expected to ask Congress soon for a first-phase national health insurance program that would cost about $15 billion to $1, billion.

Administration sources said Carter has tentatively accepted a plan to expand Medicare and Medicaid and establish an insurance program for catastrophic illnesses that mirrors the most expensive options recently presented to him.

The program also, for the first time, would limit doctor bills, and would seek limits on hospital revenues.In addition to the new federal money, the plan would add about $5 billion to private health insurance bills.

The decision represents a defeat for budget and economic advisers, who had urged Carter not to spend more than an additional $10 billion in this first step toward a comprehensive health insurance program.

The president will thus challenge Sen. Edward M. Kennedy (D-Mass.) on the left and Sen. Russell B. Long (D-La.) on the right on the persistent health-insurance issue.

Kennedy is author of a plan that would cost $28.6 billion in federal funds and $11.4 billion in private funds in fiscal 1983 and more later. Long's most recent proposal is for a bill to cover only the most costly catastrophic illnesses, those that exhaust normal health insurance coverage.

The Long plan might cost $5 billion to $10 billion a year, though the Senate Finance Committee chairman has not yet presented his dollar estimate.

In the administration, Office of Management and Budget and other economic advisers have urged the president to add as little as possible to the federal budget, and certainly no more than $10 billion.

Instead, sources said, he has made up his mind to seek a more expensive program with "something for just about everyone."

Administration officials are painfully aware, however, that Long probably holds the key to passage of any health bill in the Senate. No one will deny that the outcome by summer could be an administration-Long compromise that would simply add some help for the poor, along the lines of previous Long proposals, to an insurance package.

As of yesterday, however, the president's advisers were acting on the assumption that "he's decided on the general lines of what he wants," and any changes are more likely to be minimal.

A plan costing the government at least $15 billion to $18 billion more in fiscal 1980 dollars "is where we are today" a White House official summed up. "We do not have the final numbers. There will still be some decisions that can make differences. There are going to be some changes up and down."

According to sources familiar with them, the latest estimates, however, call for federal outlays of:

$11 billion to $14 billion to improve Medicaid coverage for the poor and near-poor and make the state-run Medicaid programs, some generous, some skimpy, more nearly equal.

Close to $1.5 billion to remove limits on coverage for the over-65 Medicare population, and remove some financial burdens on the elderly in longtime serious illnesses.

Between $1.5 billion and $2 billion to supplement employer-employe plans, to add to a newly mandated $5 billion or so in employer-employe contributions to buy uniform coverage for catastrophic illnesses. A federal health insurance standard would limit any working family's cash outlay for health care to $2,500 a year, in the most recently considered figure.

New public and private programs to prevent illness, especially in children and youths, by easing the costs of regular examinations and vaccinations. These services would be included in some of the above plans.

$2 billion a year, finally, to create the administrative machinery to run the new program and create a framework for future additions when the country can afford them.

The president has said future additions would come only then. Kennedy, who unveiled his plan with labor support on May 14, backs a system that would expand step by step once Congress has passed it.

A White House official said yesterday, "On one on the Hill thinks the Kennedy plan has any change, though Kennedy will fight hard to improve any plan that is passed." Another official said there have been no talks yet with Long on a possible adminstration-Long compromise.

But McGraw-Hill's Washington Report on Health and Medicine says the president has already "been in touch with Long personally and through key aides" on the matter of health legislation.

"We'll be taking figures up to the Hill in the next few days," to get congressional reaction, a Carter aide said. Then, if the president wants to present his plan at the same time Long starts work on his this month in the Finance Committee, he must complete it before he leaves for U.S. Soviet summit talks about June 14.