The suit names Mayor Eldridge Hawkins Jr., the State of New Jersey and the Civil Service Commission as defendants.
A Superior Court judge will hear arguments Friday morning in Newark.
The lawsuit says the loss of police and firefighters can endanger residents and claims city officials failed to have meaningful discussions with employee unions before submitting a layoff plan.
Hawkins said Thursday that the unions have the power to avert the layoffs by agreeing to contractual concessions. He said a ruling temporarily blocking the layoffs "would only delay the inevitable."