On the first day of January 1979, the Kennedy Center will owe a debt of $14.6 million to the federal government, and the Center is the first to admit that it presently doesn't have the money.

The sum is delayed interest on a $20.4-million Treasury Department construction loan that made building the Center possible.

A complex formula to refinance the loan and use the debt payments as "seed money" for arts grants was intriduced in the Senate yesterday by Sen. James A. McClure (R-Idaho).

When asked for comment, a spokesman for the Center revealed that the Center has been "intensively" exploring alternative solutions to financing the payment.

Under the MClure plan, the Center would pay off the refinanced obligation at $1 million a year and put into a "Kennedy Center Amortization Plan." The money would then, in turn, be used to finance arts grants if matched 2 to 1 from private sources. Another agency, not the Kennedy Center, would be responsible for raising the private funds.

The fully matched sum would total $3 million. A third would go back to the Kennedy Center for production costs, so that in effect the Center would get back its payments if privately matched. "The rest would go to the National Endowment for the Arts to be distributed nationally.

The bill's rationale is that Congress would be more amenable to aiding the Kennedy Center if Congress helps pay for arts in other places in the country in the process.

Reached in Houston, Kennedy Center chairman Rogers L. Stevens declined comment on the proposal because he has not yet seen a copy.

But the Center's director of operations, Thomas R. Kendrick, issued a statement that suggests the Center is studying different solutions and might not have to make an appeal to Congress.

"We have been aware of this problem and deeply concerned with its resolution on an equitable basis for many months. We are currently intensively examining several alternative approaches, one of which involves possible reworking of the basis on which we now share the cost of maintaining the Center with the Nation Park Service.

"The Center now pays the Park Service more than $600,000 annually for its share of heat and light and so forth. The Center considers the present formula inequitable, given that four of every five persons who come to the Center are visitors rather than patrons. Beyond that, Congress has charged the Center in its charter with providing substantial free educational and public service programming, much of it for those visitors.

"The Center is a 'living' presidential memorial and as such has substantially higher maintenance than conventional memorials. As a living memorial, the Center obviously must have live programming. Clearly much of it, as defined by its charter, cannot pay its way at the box office. Clearly, also, if the Center were required to pay less funds for maintenance, more money could be used to reduce capital debt without damaging existing programming."

The Center's payment to the Park Service constitutes about a quarter of the entire maintenance budget.

To build the Center, Congress initially appropriated $23 million to match private contributions, and later authorized the $20.4 million Treasury loan when inflation drove the Center's cost to $73 million.