Board chairman Melvin Rodrigue said a decision could come down from the state "by the end of the day" on Wednesday.
Layoffs are related to advertising losses due to the coronavirus pandemic. Executives say they hope the cuts are temporary.
Order goes into effect at 5 p.m. Monday.
Tests for the public begin Sunday.
City official says the centers should open to the public eventually, but the timeline for that is unclear.
Despite assurances from Mayor Cantrell that quarantined employees will get "civil leave" pay, three employees told The Lens they are currently on unpaid leave.
Defense attorneys say city's jail is a dangerous environment during an outbreak.
Schools are closed at least until April. Tests were set to begin at some schools by the end of March.
The move follows Governor John Bel Edwards' order to close bars and limit restaurants to carryout and delivery. Grocery stores, health facilities and pharmacies will remain open.
New Orleans officials are working on opening drive-through testing centers and announced the closure of libraries as coronavirus cases grow in the city.