By some accounts, feuds between the Fed's leadership and the leaders of locals representing government employees go back a generation or more.
Her supporters include heads of the locals representing 15,000 social workers, 20,000 clerical employees and 26,000 crossing guards and cafeteria aides.
Aides to Mr. Stern say he would announce at a news conference on Thursday that he had won the backing of locals representing 600,000 union members.
Mr. Ferrer, who has the backing of the city's largest unions, spent much of his day addressing locals representing health care workers, teachers and municipal workers.
Union leaders said today that his hope of achieving that continued to be distant, since it required him to win the support of locals representing two-thirds of the federation's 13.5 million members.
Large memberships give locals power-in-numbers in contract negotiations and may eliminate the inefficiency of multiple small locals representing workers in the same industry.
Among those selected were the heads of locals representing accountants, computer workers, lifeguards, emergency medical technicians and Museum of Natural History employees.
Five of the eight presidents of locals representing the 36,000 workers said that they did not support the agreement.
Mr. Stern, 45, announced last Friday that he had won the support of locals representing two-thirds of the union's membership.
Ms. Montgomery-Costa also serves as president of District Council 37, which comprises 56 locals representing 121,000 municipal workers.