Armed with new statistics showing record school enrollments, President Clinton yesterday stepped up his campaign against congressional Republicans for snubbing his plans to spend more money on education.

Clinton released an Education Department study detailing what most educators already knew: There are more students in public and private schools than ever before, a total of some 53.2 million. This number is projected to grow over the next decade, the report says, with the steepest growth taking place at the high school level.

Projections from this year through 2009 indicate a 9 percent increase, or an additional 1.3 million public high school students. In 15 states, the number of public high school graduates will grow by 15 percent.

The growth is the result of what demographers call the "baby boom echo," as members of the post-World War II generation become parents of school-age children. Clinton, hours before leaving for a two-week vacation, highlighted the surge to buttress his case for an expanded federal role in aiding local schools.

"The baby boom echo is another reason why I feel so strongly that we have to act now--to build new schools and fix old ones, to hire trained teachers, especially in math and science, especially for our high schools," Clinton said at yesterday's event, which was attended by two Washington area school superintendents, Iris T. Metts of Prince George's County and Daniel A. Domenech of Fairfax County.

Republicans last year rejected Clinton's request to subsidize school construction by giving tax breaks on the bonds used to raise money for such projects. Clinton plans to make the proposal a priority in next month's showdown with Congress over the annual budget.

Republicans are using the summer recess to build public support for their contention that there is enough money flowing into the federal treasury to justify a nearly $800 billion tax cut over the next 10 years--a bill Clinton has pledged to veto.

Clinton said such a tax cut would require reducing the federal role in education--never mind expanding it, as he wants to do--exacerbating the problems many schools are already facing. "Larger classes, fewer teachers, more trailers," Clinton said. "Sounds like a country song, doesn't it? . . . I like country music, but we can do better than that."

While taking his partisan jabs, Clinton insisted he wants to work with Republicans on a smaller tax cut as part of a comprehensive agreement on spending when Congress returns to work next month. "Yes, I'll veto the tax plan. But let's don't stop with the negative, let's make something good happen here."

Republicans said that if Clinton were sincere about wanting both to cut taxes and to address education, he would sign their tax bill when it comes to him next month. House Ways and Means Committee Chairman Bill Archer (R-Tex.) said the GOP plan would make it easier for state and local authorities to issue school construction bonds. It also would expand tax-preferred savings accounts now aimed at helping families save for college expenses to include tuition and other expenses for private elementary and secondary schools (as well as expenses such as books and computers for those attending public schools).

"We should give more parents more choices as they design the best education for their children," Archer said in a statement. He, too, balanced his criticism of Clinton with praise of bipartisanship: "And we should put students ahead of elections and work together for all of America's schoolchildren."

The Education Department study also documents a record enrollment in colleges and universities, now filled with 14.9 million students.

Clinton, one of the oldest of the baby boomers, highlighted the generational echo on a day when he is turning another digit on his own life. Immediately after the education event, his staff threw him a surprise party to mark his 53rd birthday. Then he and first lady Hillary Rodham Clinton flew to Martha's Vineyard, Mass., for their annual vacation.

CAPTION: BABY BOOM ECHO (This graphic was not available)