Garcetti was among those who voted for the changes, which defenders say are expected to bring $4 billion in savings to the city over three decades.
But last week, Greuel backed labor in saying that, although she agrees with "99.9 percent" of the changes, labor had been treated unfairly by not being consulted.
Labor, of course, isn't the only voice that matters in the race. Garcetti, who does have some support from labor, recently won endorsements from fellow councilmen Paul Koretz and Paul Krekorian. He also picked up the endorsement of long-shot mayoral candidate Emanuel Pleitez over the weekend.
Koretz, who is on the city's budget committee, announced his support for Garcetti at a famed Jewish-owned deli in his heavily Jewish district, noting the leadership Garcetti had shown during "the worst financial crisis" the city has endured in his lifetime.
"I believe that he is the right mayor to help with the budget," Koretz said.
The Jewish bloc remains a key base in Los Angeles. Although Jews only make up 6 percent of the city's population, they cast 17 percent of the votes. Garcetti already has a significant lead in the district.
Both candidates have been courting attorney Kevin James since the March 5th non-partisan primaries. James, the only Republican candidate in that race, finished third in his first run for public office.
For Greuel, an endorsement from James would help her solidify her support in the San Fernando Valley, where both Greuel and James received the majority of their votes in the primary. That support would be a welcome boost for Greuel. Though she has shown her strongest numbers in the San Fernando Valley, that dominance was threatened when Krekorian, the valley's councilman, endorsed Garcetti.
While Greuel leads among African-American voters, Garcetti's recent endorsement from the New Frontier Democratic Club, an influential African-American organization, could erode that lead as well.
The Latino vote, meanwhile, seems likely to go to Garcetti if the upcoming election follows the lead of the primary. Garcetti captured 48 percent of the Latino vote in the primary, while only half as many Latinos voted for Greuel. Current-L.A. Mayor Antonio Villaraigosa has not decided whether to endorse a candidate or not, though his cousin, state Assembly Speaker John Pérez, and Dolores Huerta, co-founder of United Farm Workers, have endorsed Greuel.
Late Wednesday, the two campaigns each announced an endorsement from high-profile Republican leaders. Former mayor Richard Riordan, who has pushed to reign in pension costs, endorsed Greuel, in what is seen as a significant coup for the city controller.
The announcement came just as Garcetti's campaign shared that Steve Soboroff, a Republican who worked in Riordan's administration, had endorsed the councilman.