Absolutely. Basically, there are two parts to the bills.
First, there's the main piece, where the US wants to expand the DMCA-takedown process for foreign sites, allowing a copyright owner to erase a "site dedicated to infringement" from all registries. There's no real indication as to what "foreign" or "dedicated" means. If DMCA actions are a good example, then dedication may be hosting a file with a suspicious name. And as for foreign, I've heard Congressmen say that .COM sites are safe, but The Pirate Bay (a BitTorrent "tracker") is a prime target in examples of why the law is needed.
The shutdown includes hosting, payment processing, search results, and name servers, for the entire domain. It's worth pointing out that when Afghanistan censored their local name servers a few years back, it resulted in random outages around the world for days as the servers tried to figure out who was right. In the end, the Afghan servers failed and were "fixed" more often than the officials could censor.
The other major part of the bills is the more troubling part. It encourages vigilantism by providers, granting them complete immunity for cutting off a site based on "credible information" that the site is hosting infringing material...or information on how to circumvent censorship elsewhere. The burden of proof is on the site owner, even if the site doesn't monitor what gets posted (a "safe harbor," under the DMCA), not to mention criminalizing helping people get information.
In other words, sound official enough in your e-mail, and you can erase Facebook from the Internet or cut off Wikipedia's donations. And we're in this, too, of course. I doubt PayPal (who handles our donations) is interested in hiring people just to investigate whether or not we're actual pirates, for example.
So, those in the United States, bug your representatives. These guys even use your IP address to point you in the right direction:
http://grassroutes.us/sopaE-mail address, Facebook account, Twitter handle, and phone number, where available.
If you're not in the United States, this affects you, too. If you run a non-US site (GAC, for example), you risk your American audience (and revenue) being cut off. And the rat's nest of treaties and political bullying will bring these laws to your shores soon enough (ACTA, for example). So I encourage you to call your representatives to explain that you won't stand for censorship and they should be pressuring their counterparts in the United States to stop this.
Douglas Adams published an article on "How to Leave the Planet," where he suggested calling NASA, then the White House to put pressure on them, then the Kremlin to pressure the White House, then the Vatican ("I gather his switchboard is infallible") to put pressure on everybody else. Which besides being very funny (with the numbers listed in the article), isn't the worst advice in the world.
When contacting your representative, (1) make it clear that you appreciate the effort (lie if you must, or at least appreciate the stress) they put in for your community, (2) give them a scapegoat by suggesting that they were misled, not wrong, in supporting bad bills ("I don't know who pitched this as a benefit to the economy..."), (3) explain your position briefly and make sure there's no factual error to pick at, and (4) in closing, play peacock and "sign" your name with a list of any credentials and positions you hold that indicate you're connected to people.