"The bill would authorize the U.S. Department of Justice to seek court orders against websites outside U.S. jurisdiction accused of infringing on copyrights, or of enabling or facilitating copyright infringement"
A court finding that a site is facilitating copyright infringement seems like a high bar to meet.
Upon some brief research (Wikipedia), it seems that Cotton's claims are true:
http://en.wikipedia.org/wiki/Stop_Online_Piracy_Act#Contents
"The bill would authorize the U.S. Department of Justice to seek court orders against websites outside U.S. jurisdiction accused of infringing on copyrights, or of enabling or facilitating copyright infringement"
A court finding that a site is facilitating copyright infringement seems like a high bar to meet.