"It's been hard fought over many years," said a spokeswoman for Unison, the country's largest union, which represents about 1.3 million workers in various professions.
In Italy, the union representing about 8,800 workers at the Italian central bank has threatened to go on strike.
Based on local union endorsements, organizers estimated that they were representing about 3.5 million workers.
The machinists represent about 20,000 workers at United and have played a central role in past takeover efforts.
District Council 37 is one of the nation's largest labor organizations, an umbrella for 56 local unions representing about 120,000 workers.
Before the Chapter 11 filing, it had asked its machinists' union, which represents about 35,000 workers, for a 7 to 8 percent pay cut.
Currently more than 80 national unions represent about 17 million workers.
The second group, representing about 10,000 workers, is the more unpredictable one.
He said the delegates represented about 180,000 workers.
The union represents about 77,000 workers, most of them black or Hispanic women.