The workers are part of Local 32BJ the Service Employees International Union (SEIU).
Failure to reach a new contract by midnight on January 1 could prompt a strike of more than 22,000 building workers at over 1,500 commercial office buildings throughout the city.
Contract negotiations between the local and the Realty Advisory Board (RAB), the industry association representing most of the city's building owners, have been underway since Nov. 15.
Hundreds if not thousands of the workers marched in Midtown after the vote.
The two sides are apparently far apart on wage and benefit issues.
"Our commercial building service workers are the highest paid in the country - and we are not asking to change that - but continued wage increases that ignore the grim economic realities facing our city and country can't continue," Howard Rothschild, President, Realty Advisory Board on Labor Relations, said in a written statement. "There has not been a strike in the commercial sector since 1996, and we are hopeful that this round of negotiations will continue the successful working relationship between the Realty Advisory Board and Local 32BJ."
The union says it will not accept management's proposal for a two-tier wage structure that would pay new hires less than existing workers.
SEIU President Mary Kay Henry says protecting good jobs will strengthen the middle class.
With more than 120,000 members, including 70,000 in New York, 32BJ is the largest private-sector union in the state.