Livewire, who was created by Bruce Timm for Superman: The Animated Series, may not be a major DC Comics villain, but she'd make a great fit for Supergirl. And, judging by shows like Arrow and The Flash, she's just the kind of villain-of-the-week that producers Andrew Kreisberg and Greg Berlanti like.
Before being struck by lightning and gaining electric and magnetic powers, Leslie Willis was a popular and controversial radio host in Metropolis, who liked bashing Superman. Because the Man of Steel was present at the time of the accident, she blames him for it and her newfound abilities, and vows to take him down.
Switching Supes out for Kara in the Livewire equation would be simple enough, and introducing a radio show like Willis' would fit right at home on the series, which will already have a heavy media presence thanks to Kara's job at CatCo.