Example of SOPA misuse (for those who don't see how it could happen):
a) A gaming site posts a scathing online video review of a high-profile game/movie/product.
b) Claiming that the video illegally uses copyrighted images, the copyright holders have the site de-listed without trial.
c) After a long and arduous process to demonstrate that the video was legally using the content under fair use laws, the site comes back up.
d) The site has no way to seek damages from the parties that wrongly accused it, and thus no way to recoup the losses incurred by being shut down during the proceedings.
e) Rinse and repeat until the small site is forced to shut down permanently due to the incurred losses... Or until they decide to stop publishing negative reviews.
This example might seem paranoid, but it wouldn't be the first time that high profile publishers have actively tried to shut criticism down (google Kane and Lynch 2), and this would give them another very nasty tool to do so with impunity... Not to mention that suing smaller companies (or individuals) secure in the knowledge that their lesser economic power won't see them through the process, even if they are in the right, is an often used tactic.
The problem, then, is not the attempt to stop piracy. The big problem is the vague language of the bill, which does not provide strict checks and balances on how the rules are enforced, thus allowing for abuse.
The thing is, and I digress, that what really is killing big publishers is not Piracy, but the Internet. Big publishers are a product of the logistical issues of the pre-internet era, where reaching a wide audience was impossible without someone handling the promotion and distribution.
Nowadays anyone can promote and distribute their products themselves, and the growing online market is slowly killing the traditional publishers (won't destroy them, but will most certainly reduce them drastically).
Piracy, in the end, is just a boogeyman used to justify measures meant to keep control over the net, and avoid the paradigm change.
Or so I think, at least.
[EDIT] Vivi22 and Dastardly posted while I was writing this.