Well the whole sell of the bill is that under the DMCA, the US copy right holders go after sites hosted in foreign countries (think Pirate Bay or other similar sites), however since they are not US based, they really have no recourse if the sites refuse to comply with the request to take down copy righted material.
So under SOPA, instead of getting the site taken down, the copy right holders want to cut off access to the site from within the US, stop google from hosting search results that point to the site, and cut off any funding from US based companies that pay them for ad hosting or payments to them (think pay pal donations).
The biggest problem is that the copy right holder only has to accuse them, and then the site has something like 48 hours to respond before action is taken. There is no burden of proof put on the accuser, and the time for the accused to respond before action is taken is too short.
Again, the RIAA and MPAA, which claim to be the biggest "victims" of online piracy are the ones funding this bill and the ones who will ultimately benefit from it.