Verizon workers in nine states could walk off the job as soon as early as Sunday, if union negotiators do not reach an agreement over benefits with the wireless carrier.

A contract covering 39,000 Verizon workers represented by two unions was due to expire at the end of Saturday. Last week the Communication Workers of America announced that 86% of Verizon workers covered by the contract voted to strike in a recent poll, if a new agreement was not reached.

The contract covers employees in nine states from Massachusetts to Virginia who work for Verizon’s wireline business, which provides fixed-line phone services and the FiOS internet service.

If there is a strike, Verizon expects its effect on customers to be “minimal”, spokesman Richard Young said on Saturday.

“We have done extensive training to prepare for this day, including the training of thousands of nonunion employees,” he said, adding that the company can also reroute calls to call centers not affected by the strike, and resolve some problems remotely.

The unions say the telecom giant is demanding that workers sharply increase their healthcare contributions and make concessions on pensions. At a rally last month, CWA official Dennis Trainor said the union’s members “reject management’s harsh concessionary demands”.

Verizon, the union says, is demanding cuts in jobs and job security and wants to either eliminate the company’s 401k benefit match or freeze its defined benefit pension. In addition, workers might be asked to pay “thousands more dollars” in health care costs due to higher deductibles, co-pays and co-insurance costs, according to the CWA’s website.

Verizon said in a statement on Friday it has seen little progress toward a new agreement after seven weeks of negotiations and called the union’s proposals “unrealistic and out-of-touch in today’s marketplace”.

The contract also affects wireline workers in Connecticut, Delaware, Maryland, New Jersey, New York, Pennsylvania, Rhode Island and Washington DC.

About 45,000 Verizon workers went on strike in August 2011 for about two weeks.