I didn't google it but I don't think many sub-500 teams have made the playoffs, have they? Half dozen MAYBE? Including strike shortened years?
Any way.. got me to thinking... what's the worst record a team could have and make the playoffs? Answer: 0 - 10, if a team tied every game of the season.
Somewhat more likely... 3-13 could make it. "Every team in a specific division losing every non-division game, then those teams splitting their own six division games 3-3. If that happened, there would be a four-way tiebreaker that would likely fall to the sixth contingency: strength of schedule." - from USAToday.