A broad coalition, including the U.S. Chamber of Commerce, Hollywood, the recording industry and organized labor, strongly back the legislation.
But consumer groups and major Web companies, including Google, Yahoo and Facebook, warn the bills could stifle innovation and censor free speech.
Sen. Ron Wyden (D-Ore.) has promised to stall the legislation when it is brought to a vote.
"The primary architects of the Internet and our leading cyber-security experts have made it clear that this legislation will undermine the key technologies that prevent fraud and protect consumers on the Internet," he said in a speech on the Senate floor on Saturday.
"Our nation’s leading First Amendment scholars have made it clear that this bill poses a serious threat to speech and civil liberties for all who use the Internet. And our nation’s leading technology employers warn that this bill presents a clear and present danger to innovation and job growth in an area that is going to be a major source of new jobs for this century."
The legislation's supporters say the opponents are exaggerating the risks and that it does not apply to legitimate websites.
The Protect IP Act cleared the Senate Judiciary Committee in May. House Judiciary Chairman Lamar Smith (R-Texas) has scheduled a third day of markup for SOPA on Wednesday.