If we also include teams that didn't ever have first place to themselves (the best they could do was tie for first), add the Indians, Padres, Phillies, and White Sox.
Not that that's necessarily a measure of hopelessness, though it pretty much was for the teams in question: Cleveland finished three games behind Oakland for the second American League wild card.
Speaking of Oakland, here are the teams that spent the most days in first place:
- Tigers, 153 days: Lost Divisional Series
- Brewers, 150 days: Missed the postseason, six games behind the second wild card
- Athletics, 129 days: Lost Wild Card