Depending on how he plays as the trade deadline approaches, I would think that the Twins could hold out for a lot. Willingham seems a little streaky, and it will be good if he can stay hot.
Willingham is 33 years old, and he may be 36 or 37 by the time that the Twins are ready to contend again. So he seems expendable.
On the other hand, if this looks like a salary dump, fans should be resentful. I would love to see a trade where the Twins deal with a smaller cap team who will give up excellent prospects if the Twins agree to eat some of Willingham's salary. The Twins could show good faith to the fans by spending some money if an opportunity arises to get one or more excellent prospects as part of a trade with a smaller cap team.