The rebuttal is this:

The bill defines "foreign infringing sites" as those infringing sites that have their domains registered outside the US, are "US-directed" and "used by users in the United States." This would include, for example, all the sites that use Libya's top-level domain, like bit.ly, but would not include a site like thepiratebay.org, as the US controls the .org top-level domain.

You can check that this is true by reading Sec. 101.3-8 and Sec. 102.1.a. (13 lines of text in total) on the Library of Congress website here:

  http://thomas.loc.gov/cgi-bin/query/z?c112:H.R.3261:

This doesn't address whether a site is "infringing" or not, but it makes it clear that sites that most people would consider US websites, like bit.ly, can certainly be affected by the bill. Cotton's argument that only foreign sites will be affected is bogus, when you look at the details of what "foreign" means.