Eyewitness News has learned from people on both sides they will keep working at the table for at least a few more hours.
The union said that so long as there are talks going on they don't plan on going on strike.
"Albertsons, Ralphs and Vons are still at the table with the union," said Christie Ly, a spokeswoman for Albertsons, in a statement. "Progress is being made, but we do not yet have an agreement. Even though the 72-hour notice period has expired, nothing has changed. The terms of our most recent contract -- including wages and benefits -- remain in place, and our stores are open to serve customers as they usually are."
Grocery store workers and their supporters held a candlelight vigil and a march Sunday night to show their resolve.
"We just want to work hard. We just want to be able to take our kids to the doctor when they get sick," said Mike Shimpock of United Food and Commercial Workers Local 770. "We don't want to go on strike but we have to stand up to these hugely profitable corporations that are trying to destroy healthcare for people that are scraping by paycheck by paycheck."
The "Big 3" chains met with workers' representatives at an undisclosed location, while union stewards spent the day passing out picket signs.
If little progress is made toward settling disagreements over health benefits, negotiators say they will tell members to walk off the job.
Both sides announced in July that they had reached a tentative agreement on the employers' contributions to pension benefits, but payments to the union health care trust fund remained a major sticking point.
Union members voted overwhelmingly to reject the health care proposal offered by the chains and to authorize their leaders to call a strike.
If a strike does take place, Albertsons will close about 100 of its stores, Ralphs will close all of its stores and Vons intends to remain open.
Los Angeles City Controller Wendy Greuel and Los Angeles City Councilman Paul Koretz marched with the workers. Mayor Antonio Villaraigosa was also out with workers earlier in the day urging both sides to reach an agreement.
A four-month strike and lockout that began in 2003 cost Ralphs and other grocery chains an estimated $2 billion.