"This is solid," said a spokesman for a dissident union who spoke on the condition that he and his organization remain anonymous.
The five dissident unions represent more than a third of the membership of the American Federation of Labor and Congress of Industrial Organizations.
Last weekend, Mr. Sweeney said, he engaged in intense negotiations with the dissident unions to try to persuade them to remain.
Failing that, the leaders of the dissident unions - which represent more than one-third of the federation's 13 million members - are warning they will secede from the federation.
The dissident unions, which include about one-third of the federation's members, are unhappy that Mr. Sweeney seems certain to win a new four-year term at the convention.
The dissident unions along with the laborers union and the carpenters union, which quit the A.F.L.-C.I.O. in 2001, have formed a competing group, the Change to Win Coalition.
In the interim, however, support for Donahue among the dissident unions (which had changed its name to the "New Voice" slate) had dissipated.
Ms. Burger said the four dissident unions needed to leave the A.F.L.-C.I.O. last summer because, in her view, the federation had done far too little to stop labor from sinking into oblivion.
It's up to the leaders of the dissident unions to make the case that what they've done actually benefits present and future union members.
The leaders of Unite Here, which represents 450,000 workers, said the dissident unions would focus on large-scale organizing drives to try to unionize thousands of workers at the same time.
