Labor leaders made a similar announcement in San Diego on Tuesday.
Workers said they don't want to strike, especially in this economy, but if it cannot be avoided, so be it.
"They definitely have turned their backs on us, and they need to turn back around and look us in the face and see how we're feeling and see what we're going through," said grocery store worker Kelly Pierce.
With more than 60,000 grocery store workers in Southern California entering their fourth month without a contract at Ralphs, Vons and Albertsons, Rick Icaza, president of the United Food and Commercial Workers Union Local 770 says the workers are ready to walk off their jobs if contract negotiations continue to stall over the issue of health care.
Union members have authorized a strike if they fail to reach an agreement.
Icaza says the corporations that own the grocery stores want workers to pay much more for health care. He says the increase would cost each employee at least $7,000 per year.
"The employers are not paying their fair share in the health and welfare benefits. It's all about health benefits this time, I guarantee it, like it was last time," Icaza said.
Tens of thousands of grocery store workers hit the picket lines throughout Southern California in 2003.
Grocery store workers say with families to take care of and bills to pay, they hope a strike can be avoided.
"If I go on strike, all it's going to do is cut my pay and I will have a hard time taking care of (my family)," said grocery store worker David Lozano.
The corporations who own the grocery stores issued a statement saying, "We are still actively negotiating and any talk of a strike is unnecessary. Our extension agreement is still in place, and we have additional meeting dates on the calendar. The only place where we can reach an agreement is at the bargaining table, and we believe our focus should be there reaching a fair and reasonable contract."
