Four of Palo Alto's five libraries were closed Thursday, as was the utilities department service center at City Hall.
About 305 out of the city's 617 employees represented by the Service Employees International Union (SEIU) did not go to work.
"They should be at work today; I'm not sure what they're doing, but I don't think that's fair, as a citizen I want them to be working," Palo Alto resident Roger Smith said.
Palo Alto is trying to erase a $10 million deficit. It is in negotiations for a new contract with the union.
"We've offered $7 million in concessions, we've offered creative solutions how we can close this budget deficit, but the city continues to reject them," union spokesperson Brian Ward said.
"The primary solutions the union is offering are more short-term based and that's probably where our biggest sticking point is, the city would like to see more structural change," city spokesperson Robert De Geus said.
The structural change involves asking the employees to kick in a percentage of their health care premium.
The city currently pays 100 percent of the $11.6 million cost, amounting to a 45 percent increase over the past five years.
"The proposal does not include layoffs at this point and we're very happy that we can put together a package that does not include employee layoffs; it's a very challenging financial situation," Assistant to the City Manager Kelly Morariu said.
Twenty-two negotiating sessions have been held since May.
"If those are the folks that are working for our city, I think they deserve what they can get, and if we do have a $10 million shortfall as you suggested, I think there's a better way to save money," Palo Alto resident Santosh Randev said.
The union estimates it saved Palo Alto $281,000 Thursday in lost pay. The employees plan to return to work Friday.
"We've shown the people of Palo Alto that we are Palo Alto, we care about Palo Alto and we want to be part of the solution," SEIU LOCAL 521 President Kristy Sermersheim said.
No new negotiations are scheduled.