In December, a Quinnipiac University poll found that Mr. Adams had seen his approval rating plunge to 28 percent. Now, with Mr. Adams facing a growing list of challengers in the June Democratic primary, there’s a “good chance” that whoever becomes permanent commissioner may not stay long, said Jillian Snider, a lecturer at John Jay College of Criminal Justice and former New York police officer.

“I’d be hesitant to take that role right now if I planned to stay in it for some time,” Ms. Snider said.