Several technology and digital rights groups have praised a U.S. Senate move toward passing legislation that would rein in the National Security Agency’s domestic telephone records collection program.

A procedural vote on the USA Freedom Act could come as early as Tuesday, with a final vote on the bill in the days following. The bill, aimed at ending the NSA’s widespread collection of U.S. telephone records, would have to pass both the Senate and the House of Representatives by the end of the year to become law.

Senate Majority Leader Harry Reid, a Nevada Democrat, filed a motion to move the bill forward late Wednesday.

Among the groups applauding the decision to move forward with the bill were software trade group BSA, tech trade group the Computer and Communications Industry Association, digital rights group the Center for Democracy and Technology and justice advocacy group the Brennan Center for Justice.

“The legal reforms in the USA Freedom Act send a clear signal to U.S. citizens and Internet users around the world that Congress is serious about reforming government surveillance practices, and providing the judiciary and the public with tools that allow better oversight over remaining narrowed programs,” CCIA President and CEO Ed Black said by email. ”The USA Freedom Act closes key loopholes on bulk call data collection and offers greater transparency, which is essential for citizens in a free democracy.”

Freedom from surveillance

Libraries have been fighting against government searches allowed under the antiterrorism Patriot Act for 13 years, said American Library Association President-elect Sari Feldman.

The Senate bill gives Congress “the opportunity to prove to the American people that their freedom from broad surveillance by their own government matters more than political posturing,” Feldman said in a statement. “It’s time, way past time, to finally vote on and pass [the] bipartisan, intelligence community-backed USA Freedom Act without weakening its already modest protections for the public.”

While the bill has a good chance of passing in the Senate, it may face a tougher test in the House, where several prominent lawmakers have suggested the legislation would hurt the ability of the U.S. government to fight terrorism. House members approved a compromise, watered-down version of the bill in May.

While top officials in President Barack Obama’s administration have voiced support for the stronger Senate version of the bill, some lawmakers have suggested the bill would endanger the U.S.

The Senate bill would require the NSA to use specific selection terms to limit its targets in the telephone records collection, and require the government to issue reports on the number of people targeted in surveillance programs.

It would give communications providers options on how to report on the number of surveillance requests they receive, and require the U.S. Foreign Intelligence Surveillance Court to appoint a panel of special advocates to argue in support of individual privacy and civil liberties during court consideration of surveillance requests.

The NSA’s bulk collection of U.S. phone records came to light in mid-2013, from leaks by former NSA contractor Edward Snowden.