The 1988 General Assembly had not been in session even 24 hours yesterday when a proposal to require a family life, or sex education, curriculum at every school in Virginia ran into a storm of opposition.

In a joint meeting of the House and Senate education committees, conservative lawmakers, many of them from rural areas, fired volley after volley at the idea.

A number said their constituents' antipathy toward legislation creating a state lottery, which passed last year, was nothing compared to their outrage at having sex education mandated in local school systems.

"People in my area are absolutely opposed to having this mandated," said Del. J. Paul Councill Jr. (D-Southampton), whose district is in rural Franklin County in western Virginia. "There's a great deal of difference between what might be acceptable in Fairfax County and Wise County," which adjoins Kentucky.

Most Northern Virginia schools already offer sex education courses, although some would be made more extensive under the proposed state guidelines.

Gov. Gerald L. Baliles supports the requirement, and said in a news conference yesterday that he will soon introduce a budget amendment providing start-up funding for the program. Administration officials did not specify the amount, but the State Board of Education estimates it would run $5.5 million.