Any prospect that Congress would put up more money to aid the beleaguered D.C. public school system virtually evaporated yesterday in a few moments of decisive banter between school board president Eugene Kinlow and Sen. Alphonse D'Amato (R-N.Y.), chairman of the Senate D.C. Appropriations subcommittee.

Kinlow read a prepared statement on the plight of public education in the United States and on federal responsibility for it. But D'Amato wanted to hear details on how the D.C. school system plans to cut spending to avert projected budget deficits of $6.4 million this year and $22 million in 1982.

Kinlow began to review various cost-cutting proposals already approved or under consideration by the board. But D'Amato, saying he was pressed for time, asked for details in writing and indicated that the hearing was over.

Kinlow wasn't ready to give up.

"We'd also like to ask the committee to take us off the hook" by increasing the school budget, he said.

"Well," D'Amato responded, "I think we have to deal with reality."

The senator smiled as he spoke and there was a ripple of laughter among the city officials and school board staff members in the committee room, including Kinlow.

"I appreciate that you see the humor, Mr. Kinlow," D'Amato said. "As they say in the vernacular. 'Nice try.'"

"Well," said Kinlow, "we had to try."

That concluded Senate hearings on the school system's proposed $248.2 million budget for the 1982 fiscal year. D'Amato made clar that Congress is unlikely to put more money in the budget. The duty of the school officials, he stressed, is to make sure they live within their budget, however difficult that may be. There was virtually no discussion at the hearing of any educational issues.

"I guess I'm naive," Acting Superintendent James T. Guines said later.

"I expected a better reception. I wanted to talk about how the test scores have gone up, about class sizes, about the value of preschool education, and we never got into that."

D'Amato said that Mayor Marion Barry's overall financial strategy of paying off the city's cumulative deficit, balancing all future budgets, and beginning to borrow on the private bond market could be thrown "out of whack" if the school system failed to live within the spending limits imposed by the mayor in his budget proposal.

The senator's questions dealt solely with how the schools plan to cut spending, not with the value or the purpose of any of the programs that might be sacrificed in order to avoid the $22 million deficit, which he termed "quite dramatic."

In his position as subcommittee chairman, D'Amato, though a freshman, effectively exercises near-total control over the amount of money Congress will authorize the city to spend.

He was the only senator present at most of yesterday's hearing and his aide was the only staff member at the table, suggesting little inclination on the part of D'Amato's colleagues on the subcommittee to challenge his authority.

When Kinlow told him that an anticipated budget deficit of $6.4 million in the current year would mostly be eliminated through a five-day furlough of all employes in September, D'Amato asked for written assurance from the board's legal staff that such a step was within the board's authority. f

For next year, said the schools' administrative officer, Shelton Lee, 700 to 800 teachers and other workers might have to be laid off. D'Amato did a quick calculatin on a piece of paper -- 700 multiplied by an annual average salary of $23,000 -- and said: "That only comes to $16 million. How are you going to make up the rest?"

"Last year we took some devastating actions," Kinlow replied. "This year the same kind of thing is facing us. We are looking at pre-kindergarten, at kindergarten. I would say the prospects for the 15,000 people in adult educatin are very dim."