A bill giving tax breaks to parents who send their children to private schools cleared the Senate on Wednesday but by too narrow a margin to overcome the veto President Clinton has promised.

While the bill received some bipartisan support, most Democrats called its benefits meager and hypocritical considering the large cuts in federal education spending wanted by Republicans in the House. Democrats instead urged support for Clinton's $12 billion, five-year proposals to build schools, hire teachers and expand after-school programs.The bill's supporters nonetheless said they would use the upcoming holiday recess to build enough public support to thwart a veto.

Sen. Paul Coverdell, R-Ga., one of the bill's chief sponsors, insisted it would "make a real difference for millions of families across America."

The $1.5 billion in breaks would lead to private savings of $12 billion, benefiting 20 million school-age children, Coverdell said.

Eight Democrats joined Republicans in the 59-36 vote for the measure, which would expand edu-ca-tion savings accounts so that tax-free withdrawals could be used for education expenses from kindergarten though college.

Sens. John H. Chafee of Rhode Island and James M. Jeffords of Vermont were the only Republicans to vote against the bill.

The House vote on the same bill last week was a more partisan 225-197, and a two-thirds majority is needed to override a veto.

The expenses covered by the expanded savings accounts would include public school costs like private tutors, home computers, supplies and transportation. Backers said most of the families taking advantage of the tax breaks would have children in public schools.

But opponents stressed that more than half the $1.5 billion in breaks over 10 years would go to people with higher incomes. The accounts are available to couples earning up to $150,000 and individuals up to $110,000, the same income limits for the original college savings bill, which was endorsed by Clinton last year.

Sen. Edward M. Kennedy, D-Mass., called the bill "an absolute sham," pointing to cuts made by a GOP-led House appropriations subcommittee Tuesday. That subcommittee sought drastic cuts in the money Clinton requested for the departments of Health and Human Services, Education and Labor. Clinton also has threatened to veto that bill.

When other provisions are considered, the education bill would cost $4 billion over 10 years. Those costs, though, would be offset by the expected proceeds of adjusting the tax code, which would leave a surplus of $24 million.

The contributions to the accounts of up to $2,000 a year by families, friends, employers, churches and other sponsors would not be tax-exempt, but the interest buildup and withdrawals would be. The current college savings measure allows only $500 in annual contributions.

The measure has other tax breaks for prepaid tuition plans and employer-paid tuition, as well as some education provisions that have nothing to do with taxes. These include creation of a program to spend $210 million on helping children learn to read, mostly by training teachers.

The bill also would give states financial incentives to use for merit pay and competency testing for teachers.

"If a family can accumulate savings and have a choice of whatever school they want their youngster to go to - as long as that youngster receives a good education, is that not really what government is all about?" asked Sen. Dianne Feinstein, D-Calif.

The House Education and Workforce Committee, meanwhile, was readying another controversial bill. By 19-18, the committee approved a measure converting nearly $2.74 billion in programs run out of Washington into grants for states and school districts.