In February 2006, President George W. Bush mandated that all over-the-air broadcasting signals would transition to digital format three years later. The National Association of Broadcasters (NAB), a group that advocates for more than 8,000 TV and radio stations, faced a daunting task: Tell millions of US residents how they can – and why they should – go out of their way to update their TV sets.

The group sought to run the effort like a political campaign, using the digital ...