You don't have to be terrible for multiple seasons to rebuild.
The problem is with the teams that are MEDIOCRE.
Case in point, the NFL's Buffalo Bills.
In the 13 years since they made the playoffs, there have been a ton of 6-10 and 7-9 seasons. That is just good enough to keep you out of the top of the draft where true superstars live. The other problem with the Bills is that they don't spend quite enough money to be largely enticing to top coaches and free agents.
The Sox have one of these problems and not so much of the other.
They have been a middling team for a while, which has kept players on a roster much longer than they should have. They have plodded along on the same course for a while, and results have been BLAH.
The good news is that they will spend money, and that can turn around a team in a fast manner. They need to bottom out, dump as much of this payroll as humanly possible (please get hot, Adam Dunn!), and start from scratch.
If they can get decent value for those players (Crain, Konerko, Dunn, Peavy, etc), they should move them. Loyalty be damned.
Bottom out, get some elite prospects from the top of the next couple of drafts, then spend money to augment that talent.
It may take a few years, but the team can be built in a rapid manner.
"Guess what? I bought you a Hawk and DJ bobblehead on ebay. It even says 'Hawk' on Hawk's hat. Isn't that cool."
---My awesome father