Bill Gault, president of the International Association of Fire Fighters Local 22, said Nutter was "playing Russian roulette" with his 2,400 members.
"What's going to happen is there's going to be a fire at one place and we're not going to have the coverage we need," he said.
"Nobody loves us till they need us. Now we're not going to be there."
Fire Commissioner Lloyd Ayers said the budget cuts "are not ideal, but beat layoffs." He said the department would spend the next week figuring out how to implement the rolling closures.
The proposed cut to police overtime, about 8 percent of the department's OT budget, was panned by John McNesby, president of Fraternal Order of Police Lodge 5.
"You can't plan crime," McNesby said. "He's trying to cut the meat to feed the fat, and it's not going to work."
The city has also canceled two Police Academy classes because of budget troubles.
Deputy Commissioner Richard Ross said dozens of cops had been redeployed from specialized assignments to patrol beats to make up for losses in the budget.
"We just have to deal with the cards we're dealt," he said. "You don't want gains that we made in crime-fighting to erode."
The city's homicide tally stood at 167 as of Tuesday, a 9 percent increase over this point last year.