To do the johnny is to 'keep walking', as per the slogan used by the iconic Johnny Walker whisky brands. The phrase refers to the act of continuing to walk a distance that would be otherwise traversed via a more efficient means, with the journey being the product of (often drunken) time mismanagement.
1: "bro, i dont think there is another train...the next bus is in 3 hours.."
2: "fuck, looks like we are going to have to do the johnny, and keep walking."
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