"When I was governor, when I saw an excessive employee pay raise, I vetoed it -- not once, but twice," he said. "I know how to stand against the storm. This is not like being a CEO, where you're in a private board room. You got the media. You've got the opposition party. You have a lot of emotions.
"We're in trouble," he said of California, a state with one of the world's largest economies and a $6 billion deficit. "California is in a mess."
Brown said companies that hire new employees should be entitled to tax credits, but he opposed Whitman's plan to give tax breaks to the wealthy.
"[Whitman is] going to cut all the taxes on the rich, like herself, and that'll somehow create jobs," he said. "That'll increase and exacerbate the gap."
A counterculture icon of the 1970s, Brown was nicknamed Gov. Moonbeam for a proposing the state buy a communications satellite.
Brown said even at 72, he has no lack of energy. He runs and does pull-ups every morning, he told Sawyer.
A former seminarian who studied Buddhism in Japan and a volunteered in India with Mother Theresa, Brown found a spiritual message in his campaign.
"Well, at the end of the day, what really is this all about?" he asked. "The fundamental quest is: How do we touch our spirituality? How do we touch that innermost part of our being? And how are we open to that same thing in other people?
"That's the intimacy, the spirituality, that you don't normally find in politics," he said. "But it's the other side. After everything quiets down, you're still yourself. And there's still life and death. When I was studying in Japan, before you'd mediate ... in the evening, someone would hit a block a few times. And then someone would intone: 'Life and death is a serious matter. Time waits for no man. Do your best.' And that, I think, could be the spirit of this campaign."