"The press" is commonly used to refer the established newspapers such as the New York Times and Washington Post, as well as smaller local (but usually corporate owned) papers. However, in the context of the first amendment it refers to printing presses. The modern equivalent would be a website of whatever type: blog, database, wiki or any other.
Censorship of open discussion with obscenity
There has been some confusion over freedom of speech and obscenity in recent times, especially as open websites (such as this one) open themselves to the posting of illegal materials. Overly strict legislation or interpretation of existing law would make attacks using such material to shut down open sites easier. This technique is already being used to ensure open sites are blocked by nanny filters, thus restricting the readership of open discussion.