In California governor’s race, the debate is over how...

California’s gubernatorial candidates are having a hard time agreeing on debates, and their disagreement is boiling down to the choice that divides much of the country:

Do you prefer CNN or Fox News?

On Thursday, Democratic Lt. Gov. Gavin Newsom accepted an invitation to debate his opponent, Republican businessman John Cox, on CNN on Oct. 1. Newsom campaign officials said they had accepted CNN’s offer not because of the national exposure it offered, but because the cable network reaches 80 percent of Californians — more than any other media outlet in the state that offered to host a debate.

Not so fast, Cox’s campaign replied. The Republican candidate has accepted debate invitations from Fox News, which has a larger national audience than CNN, and from The Chronicle and KCRA-TV in Sacramento, as part of a five-debate series Cox is proposing. Cox is also considering debate invitations from CNN and several other outlets, but has not yet agreed to the CNN debate.

Newsom, who finished eight points ahead of Cox in the June primary, is taking a typical front-runner’s attitude toward the suggestion of a series of debates: Don’t count on it.

On Thursday, Newsom declined The Chronicle/KCRA invitation for a debate in late September or early October.

“With less than four months until the general election, the lieutenant governor’s availability is severely limited due to the competing demands on his time,” Emily Swide, the Newsom campaign’s director of scheduling, wrote to The Chronicle’s editorial page editor, John Diaz.

The Newsom campaign said it received the Fox News invitation on Thursday afternoon, two hours after it accepted the CNN invite. It turned Fox down.

The CNN debate is the only one Newsom has accepted, although he said after the June 5 primary that he “would be happy” to debate Cox multiple times.

A campaign spokesman pointed out that Newsom participated in nine debates before the primary, including three that were televised either regionally or statewide.

Most of those debates, however, happened early in the campaign. As Newsom solidified his lead in the polls, he skipped several debates from February to early May, when he took part in one last forum in San Jose.

His then-rivals among fellow Democrats seethed — Fabien Levy, a spokesman for state Treasurer John Chiang, told the Los Angeles Times at the time that “any honest candidate wouldn’t be afraid to debate the issues Californians care most about, but this is another reason why voters can’t trust Gavin Newsom to lead this state as governor.”

Chiang endorsed Newsom days after the primary.

Gov. Jerry Brown, who is termed out after this year, took a similar approach to Newsom’s during the 2014 general election campaign against Republican Neel Kashkari. Brown, who held a double-digit lead in the polls, agreed to one debate — without an audience, in the small Sacramento TV studio of the California Channel, a statewide public affairs network. It aired on the opening night of the NFL season.

Joe Garofoli is The San Francisco Chronicle’s senior political writer. Email: jgarofoli@sfchronicle.com Twitter: @joegarofoli