The union — which represents more than 900 workers, including library staff, secretaries, teacher assistants and special-needs teacher assistants — rejected the offer Monday night.
Debbie Engel, chairwoman of the school board, said both parties are in agreement on all issues, except compensation in the second year of the two-year contract.
The union wants a fixed amount in that year, while the board says it can't because it could end up cutting in the classroom.
Engel says she remains hopeful the situation will resolve itself soon.
Danny Burrell, who speaks for the support workers, says negotiations will continue and striking workers will be back on the picket lines Tuesday afternoon.