"To see them up close in a real setting where we discuss and we grapple with these tough issues," he said. "We've seen the attack-dog politics, we're going to see some more, but I certainly think that the customary tradition of candidates debating, discussing and being accessible in real time, in a live setting, is the way to go from here on out."
Brown is hoping Whitman will go along with his debate idea. She has not yet responded to his challenge.
"We're going to give him a real challenge," said Whitman at a rally Wednesday. "And you know what? We're going to talk about the things that matter most to California: We're going to talk about creating and keeping great jobs in California."
Brown is citing his experience as a two-term California governor.
"It's not going to be done like a CEO slashes jobs and outsources them to foreign countries," said Brown. "This is the people's government -- the schools, the police, the health care."
Brown talked at the conference about where he would cut to balance the state budget.
"Where would I start? I would start in the governor's office. I'd cut as much out of it as I could. I'd go to the legislators, start taking out the perks, the staff. We've got to reduce this thing in a very austere way."
Whitman was less specific, but pointed in her criticism at the rally.
"Elections cannot be bought, but candidates can. And Jerry Brown is bought and paid for by the union bosses," said Whitman.
Brown has had a career in politics. He easily won the Democratic nomination, beating out several little-known candidates. He was California's governor from 1975 to 1983, and he also served as secretary of state and the mayor of Oakland.
The former eBay CEO is a newcomer to the political arena, but she's now a step closer to becoming California's first female governor.
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