The state's board of education has agreed to work with Governor Bush to try to overturn the measure, which is enshrined in Florida's constitution after being approved last November by 52 per cent of voters.
Bush, the president's brother, says the state simply cannot afford it and that the cash is needed for improving teachers' salaries and literacy programmes.
"This past year, we increased education funding by more than $800m, only to see around half of it go toward the class-size amendment," he said. "In light of the tremendous cost and minimal return on investment for students, the best solution is to allow voters a chance to repeal this obstacle to quality education."
By 2010, class sizes must be capped at 18 pupils for kindergarten to third grade (ages five to nine), 22 pupils for fourth to eighth grade (nine to 14) and 25 in high schools (ages 14 and above). Over the next eight years, schools will be compelled to reduce class sizes by an average of two students per year until the target figures are reached.
The board of education has warned taxpayers to expect to pay up to $27bn for the new schools, classrooms and extra teachers needed, plus up to $1bn a year in operating costs.
Republican state senator Burt Saunders is seeking to collect half a million signatures on a petition by next August, a total that would allow the measure to be placed before voters for a re-think.
He is being backed by Governor Bush and the board, reigniting debate over Florida's class sizes, which are traditionally among the nation's highest.
John Bowman, executive director of Florida State University's Center for Education Innovation, said other states will watch developments with interest.
"What happened in Florida will be a watershed nationally. It's one of the most ambitious projects in class-size reduction ever undertaken and the cost is staggering.
"If it's repealed, it will send a clear message to other states about voters' priorities in education."
In 2002, Florida's pupil-teacher ratio of 18.4, calculated by including support staff and administrative assistants, was the sixth-worst of the 50 states, with only Utah (21.8), California (20.5), Arizona (19.7), Washington (19.6) and Nevada (18.5) reporting a higher figure. The national average is 15.9.
Said Sharon Lettman-Pacheco, deputy director of People for the American Way, an education pressure group that sponsored the original amendment:
"The voters made it clear last year that education was their top priority but unfortunately the governor's refusal to accept the will of the people, and his picking and choosing which votes he will honour, means that Florida's schools and children will suffer."
Darryl Figueroa, spokesman for the National Education Association, which represents 2.7m teachers, agreed: "Teachers and parents are going to be pretty unhappy if this is repealed. Pupils will always perform better in smaller classes."
While supporting smaller classes, however, the Florida School Boards Association says sports and extra-curricular activities in schools are already suffering from the fiscal squeeze.
Its president, Andy Griffiths, said: "We're providing A-plus schools on a D-minus budget."