Backer Marco Rubio said the Senate "should take more time to address the concerns"
Eight US lawmakers have withdrawn their support for anti-piracy laws, after "blackout" protests on thousands of internet sites.
Two of the bill's co-sponsors, Marco Rubio from Florida and Roy Blunt from Missouri, are among those backing away.Online encyclopaedia Wikipedia and blog service WordPress are among the highest profile sites to block their content.
The Motion Picture Association of America (MPAA) has branded the protests as "irresponsible" and a "stunt".
The MPAA, Hollywood's primary advocate in Washington and a key supporter of the legislation, is led by former Connecticut Democratic Senator Chris Dodd.
Both bills focus on responding to online piracy, specifically illegal copies of films and other media.
The bills would also outlaw sites from containing information about how to access blocked sites.
The BBC's Jonny Dymond says that with Mr Rubio and Mr Blunt withdrawing their support, the Senate bill - Protect Intellectual Property Act (Pipa) - that had looked likely to pass, now appears to be in trouble.
Mr Rubio is a rising star in the Republican party, and is often suggested as a viable vice-presidential choice for this year's Republican presidential nominee
