The Communications Workers of America represents about 160 of the 700 workers employed by the Red Cross' Greater Alleghenies Blood Services Region based in Johnstown, Pennsylvania.
The union earlier this month filed a 20-day notice of the planned strike over a management proposal for blood collectors, drivers and others to pay more for their health care benefits.
Recent negotiations failed to produce a new contract and no new talks were scheduled.
The Greater Alleghenies Red Cross supplies blood to parts of Pennsylvania, Maryland, Kentucky, Ohio, Virginia and West Virginia.
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