There was! The original video, which never made it to the public in its entirety, featured the band performing the song in a flooding basement, and was directed by Jason Matzner. A snippet of it can be seen here. Mark revealed in a 2013 Reddit AMA:

I had an idea for the ‘Josie’ video, that we would be the band playing on the deck of an old cruise liner as it sunk. We would play in real time as everything around us exploded in slow motion. Gradually at first, building in intensity, reaching complete catastrophe at the end. People running, sparks flying, superstructure collapsing. The ship floods, and the last shot of the video is the ship sinking into the dark waters as the song ends “everything’s gonna be fine.” The label listened and said “cool, but no. That video will cost millions of dollars.” So the alternative was us playing in a basement and the pipes break. The room floods and we continue playing. We shot the video in the backlot of universal studios on a very cold and long day. I just remember shivering and the water always being shockingly cold every time we had to get in it. Bracing. So cold. The first edit came back and no one was really feeling it, so we scrapped it and started over.