The argument against SOPA is not that sites could be shut down, but that there needs to be a very demonstrable reason for it--with warrants and evidence and judges signatures. With SOPA, the site can be shut down based on accusation alone, and THAT is the problem.
The U.S. Constitution has all these nice phrases like "due process of law" (see 5th Amendment), but they don't really mean anything if the government can take your property away without your having been convicted by a jury in a fair trial where you had adequate legal representation. Nothing terrible would happen if the government were to leave the web site up until a jury convicted these people.
If you were accused of a crime, wouldn't you want to have a chance to defend yourself in court before you had your property taken away?
It's the same basic principle.
The point is, there's stuff like formal charges, warrants, and so on which have to be taken care of. The cops can't just impound your car because someone said you were using it to ship stolen property - they need to get a warrant.
Fully half of the bill of rights concerns freedom of expression or due process. SOPA was an attempt to rip that away, to stamp the internet as a constitution free zone. Considering that the internet will soon be the primary backbone of industry, personal and business communication, and the dissemination of news, that is a very dangerous development if we wish to preserve individual liberty.