Leaders of the Service Employees International Union sent out ballots earlier this month. Some 95,000 SEIU members have been without a new contract for more than a year.
Now, they're upset because they're being forced to take a required three days off without pay.
No state employee union has ever called a general strike and it's unclear what would happen if one did. Government officials say a walkout by employees would violate labor agreements and the state would punish anyone who strikes.