Mr Jones is unrepentant about the attention he is getting, saying Labour had asked for a contest and he had delivered. He describes the effect as "detonating the cosiness between the two primary candidates".
One of the reasons people think twice is the concern that he will put off female voters.
Mr Jones says he can't hide from the "dramas that have hobbled my career" and accepts that he will not be supported by some women in Labour's caucus.
He does not believe that the same view is held by women in general. During a walkabout, it is the women who toot and wave at him.
"Round Aotearoa I've always found I've been very popular with women. I've never been at the top of the hit parade with feminists. But the women I want to appeal to are the women who read the Woman's Weekly, not Germaine Greer."
He has resisted making the same big ticket promises as the others, saying what separates him from them is that he will not make unaffordable promises.
He describes the campaign as "a journey to redemption" for him, a chance to show he does deserve the "potential leader" tag that he was given from the start, despite his subsequent mistakes.
He observes that people love supporting the underdog.
"I am more popular, probably, among Kiwis who didn't vote Labour last time. I genuinely believe that by the end of this race, I will be the public champion."
He is unrepentant about his strong views. One is his support for the mining industry. "I'd rather have the young people of the north with a shovel in their hand than wandering around picking locks."
He says this should not be a shocking stance from someone in the Labour Party, as it was born from mining.
The other related issue is his view of the Green Party, which Labour may well need for a coalition. Mr Jones says his primary goal is to ensure Labour's polling has "a big fat 4 in front of it, not a half-baked 3". That entails recovering votes from the Greens.
"I want to see little brown Kiwis staying at home and not going to Australia. If that means offending the Greens from time to time, such is life."