The City Council voted last week to lay off 80 of the city's 776 officers to help the city close its $31.5 million budget gap for the fiscal year that begins Thursday.
Layoff notices were sent out on Monday and the layoffs would become effective on July 12 if the police union doesn't make concessions by then.
Council members want union members to contribute 9 percent of their pay toward their retirement benefits, just as other city employees do.
But the union says that last year its members already agreed to $34 million in givebacks over three years, and is seeking to have their jobs guaranteed if they agree to further concessions.
Police Chief Anthony Batts said last week that if the 80 officers are laid off, his department will have to focus on its core operations, such as responding to 911 calls, and some specialized units may have to be reduced or eliminated.