My younger son and I were looking at this page, of quarterbacks who have had a passer rating of 0 in a game. Now, it turns out that the NFL artificially caps how low you can go by not letting anything you do count for less than zero, no matter how bad it is. (For instance, part b of the formula is ((yards / attempt) - 3) * .25. Clearly, if you have three yards per attempt, you get a zero -- but even if you have -20 per attempt, you also get a zero.
Well, we didn't do all the calculations to see how low anyone would have gone were the zero floor removed, but here's our candidate:
Versus the Bengals, on 12/12/1976, Joe Namath went 4 for 15 passing, for 20 yards with 4 interceptions, which we figure earned Joe a whopping -848 passer rating for the game, if there was no floor.
Interestingly, the Jets yanked Namath, and his replacement, Richard Todd, also had a zero passer rating that game!