There are many reasons so many folks who work the web are opposed to these bills. Beyond the fears of enshrining government sponsored censorship (ala China) which could easily kill your access to non-American news media (especially important in a crisis) and stifling innovation (by creating a precarious legal climate for startups), existing businesses models that allow users to link to content (youtube, twitter, flickr, imgur, you name it) could be put off the internet in one fell swoop at the whim of another industry. But theres another way to look at this issue - the economics of it don't make any sense. All signs point to this as being a massive lobbying effort by the publishers and movie industry to break the web once and for all and theres a great article by Julian Sanchez (of the Cato Institute) on Ars Technia discussing the economics of piracy which goes into great detail exploring the claims of the RIAA and the movie industry for the supposed harms of piracy.
Some of the more salient points from the article include that the only evidence for harm is coming from these industries themselves, when, during a time of great economic distress for the nation these industries are doing quite well - in fact their profits and CEO compensations were up last year. The fact that they have had some layoffs (as most industries have) may be explained by the fact that they aren't making moving in the US anymore, but have instead outsourced them to cheaper locales (Canada and Australia). The main purpose of copyright is not to protect the creator of a piece but to encourage the production of new content. Copyright is a tool used by the goverment to obtain an end, and the end here is supposed to be to foster creative industry. Sanchez looks at the creative output of publishers and the movie industry and finds that if anything they are currently even more productive than in decades past! The GAO has stated that quantifying the effect of piracy on these industries is difficult if not impossible.
Sanchez acknowledges that the effect of piracy on the older publishing industries may be negative, but the question he raises is whether or not the effect is really bad enough to warrant new laws which may end up having lots of other (perhaps unintended) negative consequences down the road. Besides, the whole analog to "theft" falls on its face with digital piracy. Unlike food and widgets for which a greater demand creates more jobs (as chefs and widget makers), more sales of digital products (at least online) just generate more profits and not necessarily any more jobs at all because making a million copies of a digital product costs essentially nothing. Sanchez points out, I think rightly, that Netfix and Hulu probably have done more to stem piracy than any law that could be passed, and its simple to see why. Each person has a limited number of hours to consume media - if you can provide enough to satisfy casual consumers easily and cheaply they wont seek out additional illegal sources. And when taking the family out to the movies can easily run $80, $9 for Netflix seems a lot more reasonable.