The strike would be the second work stoppage on Broadway in less than five years; the musicians’ strike in 2003, which lasted for four days, was the first time since 1975 that Broadway was shut down by a labor dispute.

Many in the industry saw this confrontation coming. In past negotiations, the league, which is made up of both producers and the theater owners to whom they pay rent, has been weakened by its natural divisions. But the league has determined that this would be the year they made major changes to rules they find frustrating, and early in the talks, it seemed ready to lock the stagehands out to force the issue.

The talks, which have been going on since before the union’s contract expired in July, broke down over the issue of work rules. The stagehands contract has strict rules governing how many stage hands must be called to work, what kind of tasks they can perform and how long the work-calls last. Union officials have said the rules are in place for safety and to keep stagehands from being exploited by their employers.

League members, which say the rules inevitably lead to long periods of time when stagehands are on the clock with nothing to do, have been pushing for more flexibility in deciding when and how many stagehands are needed and have offered a package of raises in return for more control.

James J. Claffey, the president of the union, has said that the stagehands would be willing to make changes to the rules in return for benefits of equal value. But there is no way to tell how much work the stagehands would actually have under the rules the producers are proposing, Mr. Claffey said, and so it’s difficult to gauge the value of what the league has been offering in return.