CDT, a major critic of past versions of the bill, said "good progress has been made" with the proposed amendments. However, the bill still falls short because it would still allow companies to share information with intelligence agencies such as the U.S. National Security Agency, and it would allow government agencies to use shared information for purposes unrelated to cybersecurity, the group said in a statement.

CDT will not oppose the bill in the House "in deference to the good faith efforts" made by its sponsors to address privacy concerns, the group said. The group will push for amendments in the House and in the Senate, which would next consider the bill if it passes the House.

Rogers predicted the bill will pass in the House when it's . "What we're trying to do now is make sure there's a comfort level, a transparency about what we're trying to accomplish," he said.

In addition to the limits on agency use of the shared information, a new amendment would require the federal government to notify a private company if it shared information not related to cyberthreats, either deliberately or accidentally. Another amendment defines the type of information that can be shared, with a focus on network vulnerabilities and disruptions, Rogers said.

Rogers noted that support the bill. "There's a reason every corner of the private sector loves this bill," he said. "They need the help, and they need it now. They're absolutely under siege."