My understanding is that the bills are giving copyright holders greater power to enforce their property rights, which would impede the flow of information. I forget which bill it was, but one of them wants to reduce the levels of infringement to two. There are currently three levels of infringement carrying different court sanctioned penalties. Non-willful infringement (there is no proof that the website owner deliberated intended to break the law), ordinary infringement (I don't know what this is to be honest), and willful infringement. Willful infringement carries criminal indictment and can potentially cost a lot of money in sanctions (I don't think there is a any jail time... may be?
Copy right law is constructed to balance the rights of copy right owners and the rest of society. To that end, there are clauses in there, such as 'fair use' and 'archival rights', that allow institutions, such as libraries and schools, to run. In the real world, interpreting 'fair use' isn't always obvious. But the proposed law wants to take out ordinary infringement and define wilfull infringement in terms of what the judge deems reasonable expectations. So even if you genuinely did not know any better, if the judge thought a reasonable person should of known better, that automatically makes you eligible for criminal indictment and huge fines. There is no middle ground. The American Library Association is worried that libraries and schools are going to self-censorship them selves basically as a risk/benefits analysis. You could be interpreting 'fair use' in a legal way, but if the judge thinks otherwise, the liabilities may far out weigh the benefits, therefore, just don't do it.
That is one aspect of the proposed law, anyway.