Negotiations between the employer Broadway League and the American musicians' union section 802 are entering a new round of mediation on Wednesday.
"If we do not have a new contract by Thursday morning at the latest, we are prepared to strike immediately. We hope that we can reach an agreement", the union writes in a statement.
The musicians on Broadway have been without a collective agreement since the end of August and want to see improved conditions regarding salaries, healthcare benefits, employment security and working hours.
Actors' equity association, which represents theater actors and stage managers, recently reached a preliminary agreement with Broadway League on these issues.
Among the twenty-odd performances that would be affected by a strike are "Hamilton", "The Lion King", "Wicked", "Mamma Mia", "Chess" and "Chicago".