Union leaders say Verizon workers will stay on the job.

This despite their current contract expiring at midnight last night. 

The Communication Workers of America union says the nearly 39,000 Verizon workers will continue their fight for an agreement.

A recent poll from the union found that 86 percent of workers supported a strike over a new contract. 

The telecom giant is demanding workers increase their health care contributions. 

The employer also wants to reduce pension payouts. 

Verizon says it's training non-union workers to fill in—in the event of a strike.