Elmore spoke Tuesday to an audience of more than 60 people at the Palmetto Electric Cooperative building on Hilton Head Island.
The meeting was organized by the Democratic Club South of the Broad.
The association, which represents the school boards of the state's 85 school districts, is opposed to the proposal called "Put Parents in Charge," Elmore said. Statewide, many school boards have passed resolutions opposing the plan, she said.
Individual members on some school boards support the plan, she said, but she knows of no board that, as a whole, has passed a resolution supporting it. She also said it isn't something parents are demanding.
"The issue isn't coming from the grass roots," she said, "It's not something the public is crying for."
Instead, the plan is being pushed by some state legislators. "It's a top-down plan," she said.
Under the proposal, families who earn $75,000 per year or less could get a dollar-for-dollar tax credit against their state tax liability for private-school tuition or to compensate for the expenses of homeschooling.
The upper income limit is a problem, she said, because it would make the tax credit an option for 96 percent of families in the state.
Another part of the plan allows the creation of nonprofit organizations called scholarship granting organizations, which would provide low-income students with scholarships to attend private schools.
Individuals and corporations could donate to the organizations and take a dollar-for-dollar tax credit up to the amount of their tax liability with the state for the amount they donate.
Before the meeting Tuesday, Elmore said that even if the only families who take advantage of the proposal are those whose children already attend private schools, the state will lose $208 million in state taxes in the next five years.
Those are dollars needed not only for education but for other vital state services, such as mental-heath and road improvements, she said.
Another problem with the plan is that private schools are not accountable to the public for students' academic achievement, she said.