Christopher Lacovara, 17, looked across a table at Secretary of Education Terel H. Bell yesterday and quietly challenged one of the basic tenets of the Reagan administration.

"I agree that education is a responsibility of the states," he said. "But many states are struggling for their economic lives. Perhaps the states will go below a certain level. Then will you let the states sink?"

Bell listened carefully as Lacovara spoke, then rejoined: "I think most of the states are in a lot better shape than the federal government. The control and financing of education, we think, should be as close to the people as possible. We think the best thing the federal government can do to help local schools is strengthen their tax base."

Lacovara, who lives in Northwest Washington and graduated last week from Gonzaga High School, is one of 141 presidential scholars chosen by a commission as the top high school seniors in the nation. Yesterday, he and the other award winners spent two hours with Bell and his aides talking about American education in an ornate Jacobean theater at the Folger Shakespeare Library.

The encounter between President Reagan's top education official and the students chosen by a presidential commission as the nation's best was often a prickly one. Many of the students complained about budget cuts and argued for more federal aid to education, while Bell strongly defended administration policies.

The high school seniors were chosen for the honor, which includes a $1,000 prize, a bronze medallion, and a five-day trip to Washington, after a nationwide search that started with the test scores of about 2 million students.

One boy and one girl were chosen as the top academic students from each state, the District of Columbia, Puerto Rico, and from Americans living abroad. Fourteen more were chosen at-large, and 21 were picked in a separate competition for talent in music, art, dancing, acting, and creative writing.

Besides Lacovara, whose father, Philip, served as an assistant Watergate prosecutor, the winners from the Washington area include Katherine L. Chen, from Immaculata Preparatory School in Northwest Washington; Orde F. Kittrie and Ann A. Lofquist, both from Walt Whitman High School in Bethesda; Gabriel C. Paulson, from Kennedy High School in Silver Spring; Stefan G. Christian, from J.E.B. Stuart High in Falls Church, and Mark C. Wilkins, from South Lakes High in Reston.

Chen has studied Latin for five years and worked in a bakery after school. Paulson said he is a devout member of the Russian Orthodox Church, studied three years of physics, rides to school on a Yahama 350 cc. motorcycle, and works as a car mechanic. Kittrie, whose father is a law professor at American University, is a ranked National Rifle Association sharpshooter and president of his high school chapter of Amnesty International.

"These are some of the most outstanding students in the country," said Beverly Fisher White of Florida, chairman of the 49-member commission. "They show what American education can do."

But when they spoke to Bell many of the students seemed dissatisfied.

For example, Mark W. Pinkosh, 18, of Hawaii, complained that he wouldn't be able to go to New York University to study drama next fall because of uncertainty about federal student aid. "Your polices may not be creating problems for hundreds of thousands of students, as you say," Pinkosh told Bell, "but they've kept me out of the school I wanted to attend."

The audience clapped loudly, but Bell replied, "Maybe the aid program we have isn't posh enough for you to go to NYU. But you can make it at the University of Hawaii.

"I'm part of a conservative administration and I'm proud of it," Bell added. "Some of you would have different views. But I would just remind you that we won an election in 1980 and that was an expression" of what voters want.