I'm not sure how much actual airplay this got, but it was on MTV in the early 90s. I've heard it described before as the best example of the "anti video", this is to say a video made by a band who abhorred the MTV aesthetic but understood the medium as a promotional tool. On Let It Be, they had a song called "Seen Your Video" that referred to popular music as "phony rock n' roll" (which it was), and years later when they were faced with the decision to buy in or sell out, they gave it away with their fingers behind their backs. What a great band.
I'd heard the Replacements were getting back together last year to support their greatest hits record (that they recorded a new track for). I was super stoked as it was right when I moving to the Chicago area and I figured that if they happened to play any dates outside Minneapolis, this would be it. Sadly, nothing materialised, but I've still got my hopes up. For the hell of it, here's a live version of a song on their first record, "Johnny's Gonna' Die" (about Johnny Thunders...it's a very bad introduction the band, but it's great if you're already into them) dated 1981:
Here's another one from the same show (the internet is great!):