The former San Diego mayor is one of 46 candidates who appear on the ballot for next month's recall election.
Faulconer said that the vaccine is the best way to bring the COVID-19 pandemic to an end when inquired about masks in schools.
"The insiders at California Republican Party are now no better than the Democrats," according to Cox's campaign.
One of the two proposed debates would be televised by the Spanish-language network Univision, Kevin Faulconer said Monday.
His song "What Would You Do?" is about police brutality and racial discrimination in the U.S. justice system.
California gubernatorial candidate Kevin Faulconer said the lack of progress in fixing problems at the state's Employment Development Department is "shocking."
"It doesn't matter who the candidates are," Democratic strategist Garry South said of the recall effort targeting California Governor Gavin Newsom. "Newsom is going to beat it on the first line anyway."
The already crowded field for a potential recall election continues to grow.
Faulconer said he wants to eliminate California's state income tax for individuals making up to $50,000 a year and households making up to $100,000, in an effort to make the state more affordable for the middle class.
Organizers have obtained enough verified signatures to trigger a recall election for the governor in the fall.
The election is likely to take place in the fall and aspiring contenders have another 58 days to announce their campaigns.
Kevin Faulconer, the former mayor of San Diego, deflected questions about if he would want the former president's backing in California.
In past efforts to recall a California governor, signature verification hovered between 40 and 60 percent