Because her father is a federal worker and her family lives on federal property, Amy Carter's enrollment at Stevens Elementary School will result in the District of Columbia public schools collecting $931.62 in federal aid this school year.

The rationale for that payment is that the District government collects no property tax on Amy's house at 1600 Pennsylvania Ave. NW, and that local government is doubly penalized because her father also works there and therefore his employer pays no school taxes, either.

Amy's father, however, like every President since Eisenhower, views the $800 million annual impact aid program as wasteful and misdirected, and he wants to reduce it.

Other critics of the program suggest that while the city can't collect property tax on the White House and other federal installations, it benefits indirectly from money spent in the area by highly paid government employees.

Business establishments frequented by employees lured to Washington to work for the government collect sales taxes that help support operation of the city's schools, they say.

But no President has yet been able to persuade Congress that the program should be abandoned, perhaps because there are Amy Carter-counterparts (beneficiaries of impact aid) going to school in 411 of the nation's 435 congressional districts.

The lobbying effort that has sucessfully repelled Presidential attacks on the program, even when it required overriding a veto, is directed from a sparsely furnished, bare-walled rented room of a Capitol Hill row house.

The Washington office of Impacted Area Schools doesn't need a plush-carpeted, paneled board room of an uptown law firm to work its magic on Congress. "We've got clout where it counts, back home," explained Lanston E. Eldred," a consultant to the loosely-knit national organization of the 4,300 local school districts that receive impact aid funds.

"Superintendents, board members, teachers, PTAs, tax assessors, they do most of the lobbying," Eldred said. "Occasionally they'll have to come to Washington and raise hell when there is a veto to be overriden."

"When a new President takes office," said Dr. H. David Fish, president of the national impact aid organization, "He wants to put his stamp on a new program, so he looks for a place to cut. He goes to HEW and asks for suggestions and some bureaucrat pulls out the impact aid file."

Fish, who is special projects director of the San Diego schools, said the administration then uses impact aid as "a loss leader. They know we'll come out of the woodwork and beat them, but it allows them to go ahead with new programs in education on which a new President can enhance his image."

"People in San Diego can't understand what the problem is," Fish added. "They say, 'if the federal government is a property owner, why shouldn't it pay'" to help educate the children of workers brought to the area by the government facility.

Fish acknowledged that much of the criticism stems from the fact that the wealthy suburban school districts in the Washington area are among the major recipients of the aid.

"But Washington is a typical," Fish said. "Out in the boonies, the money is vital. It's not a game. To many school districts, it's essential for survival."

To answer some of the criticism, Congress in 1974 approved what was known as the "Montgomery County amendment" to the program. It called for the gradual elimination of aid to schools that educate children of federal employees who work outside the state where they live.

The action removed from eligibility 14,000 of the 26,000 children of federal employees in Montgomery County, according to Dr. Paul Henry, who administers the program for the school system.

Henry, who also is national treasurer of the impact aid organization, said he fears the Carter administration will seek further legislation in 1978 that will affect Montgomery, Fairfax, Prince George's and other school systems in the Washington area.

One rumored change, Henry said, would removed from eligibility children whose parents work outside the county (not just the state where they live.

Such an amendment would remove another 3,000 children in Montgomery from eligibility, Henry said, but would have even more far-reaching effects in Fairfax, "because of all the people who live there and work at the Pentagon" which is in Arlington County.

Impact aid was enacted in 1950 to ease the burden the federal government imposed on some school districts because children were being sent to schools by parents who either worked or lived on federal property, or both, and therefore did not generate any property tax revenue.

Over the years, despite presidential opposition, Congress has broadened application of the aid, most notably in 1974, when it began to make payments in behalf of children who lived in federally assisted public housing projects.

As a result, New York City, because of the large number of students who live in public housing there, is now the largest recipient of impact aid, getting $21 million this year.

Area school systems nonetheless remain major benefactors. Fairfax County ranks second, with $11.6 million; Prince George's, third, with $7.8 million; Montgomery, seventh, with $4.9 million; the District, ninth, $4.5 million; Anne Arundel, 11th, $3.4 million; Prince William, 18th, $2.5 million; Arlington, 37th, $1.5 million, and Alexandria, 67th, $1 million.

Speculation about what the Carter administration will propose is based in part on recommendations contained in a draft letter circulated on Capitol Hill earlier this month.

But HEW Secretary Joseph Califano said that draft "was not circulated by me or seen by me or any senior staff person. We don't have a final proposal."

Califano said his opposition to the program, which dates back to his days as an adviser to President Lyndon B. Johnson, "is on the way the aid is distributed. Millions of dollars are going not to where there is need, but to affluent areas with adequate tax bases."

Califano said the administration "wants to trim back so the program is fair" while still "meeting enough of the political objections" so the changes will get through Congress.

An alternative to the present formula that is popular with area representatives Congress would replace impact aid with payments to local jurisdictions in lieu of taxes on federal property.

Maryland tax accessors have calculated that federal installations in Montgomery County, which include National Institutes of Health, the Bureau of standards and the Department of Energy, have an appraised value of $318 million. If they were taxed at existing rates, they would generate $12.5 million a year in general fund taxes, about half of which are used for schools.

Rep. Marjorie Holt (R-Md.), whose district includes Ft. Meade, Andrews Air Force base and the Naval Academy, is a conservative who might normally oppose federal aid to education.

"But it's critical in my district," Mrs. Holt said, "Those of us who depend on it can't afford to give it up," although she also would prefer a payment in lieu of taxes.

"I can see the inequities, and that's what the presidents always see," Mrs. Holt said. "There are some very bad examples, for example, Montgomery County, where there is very little land off the tax rolls, but many federal employees. They are homeowners who pay taxes, so the county is getting twice as much aid.Montgomery can stand the loss, but my district can't."

Rep. Gladys Noon Spellman (D-Md.), whose district adjoins both Steer's and Holt's, figures "we'd be way ahead" with payment in lieu of taxes.

"It's not a handout," Mrs. Spellman said. "We wouldn't have the problem if the government weren't a free-loader."

Rep. Robert H. Michel (R-Ill.), a long-time critic of the program, told the House Subcommittee on Elementary, Secondary and Vocational Education last summer that impact aid is outmoded. It benefits only 25 percent of our school districts and the expense of the other 75 per cent. I am convinced that if the three-quarters not receiving this money ever fully understood how their tax dollars are used, they would rise up in arms."

Michel cited a 1969 study of the program by the Battelle Memorial Institute that found that heavily "impacted" districts tend to have a lower ratio of pupils to teachers; higher per pupil expenditures and lower tax rates than districts not included in the program.

"The effect is to allow a better level of education with less local effort," the report found.

As a practical matter, without impact aid, the average Fairfax County homeowner would have to cough up an extra $68 a year in property tax, according to Rep. Herbert Harris (D-Va.).

While the debate continues about the equity of the program, even its harshest critics recognize that the federal government can impose a hardship on an area.

"The only part of impact aid program that can be justified," said the Battelle study, "is the section providing payments for Category A children, who live on a military base or other federal facility but attend public schools in a community.