The bill is meant to improve information-sharing about cyber threats between companies and the government, with the goal of helping to thwart cyberattacks. It would let the government share classified information with companies to that end, and also provide liability protection for companies so they are not subject to lawsuits for sharing data about cyber threats.
The White House said last year that it would veto the bill, over fears it could lead to corporate or government intrusion into private emails or other personal information in an effort to track down cyber threats.
This week, the White House signaled it cannot fully support the bill, but stopped short of threatening a veto.
"We continue to believe that information sharing improvements are essential to effective legislation, but they must include privacy and civil liberties protections, reinforce the roles of civilian and intelligence agencies, and include targeted liability protections," the National Security Council said.
The council said it wants to keep working with the House on the bill as it moves forward.
The House Rules Committee set a deadline of next Tuesday for members to file amendments to the bill. The committee will also meet Tuesday to approve rule for the bill; once a rule is approved, the House will be able to consider the bill on the floor as early as the next day.
The House will take up other bills next week on cyber issues, although these will be suspension bills that will get less debate and will need to be approved by a two-thirds majority vote. Those bills, which will not require a rule, are:
H.R. 756, the Cybersecurity Enhancement Act, from Rep. Mike McCaul (R-Texas), to boost cyber security research.
H.R. 967, the Advancing America's Networking and Information Technology Research and Development Act, from Rep. Cynthia Lummis (R-Wyo.). This bill is aimed at aiding information technology research.
H.R. 1163, the Federal Information Security Amendments Act, from Rep. Darrell Issa (R-Calif.). This bill is aimed at creating an updated cyber security framework for systems that support the federal government.
— This story was updated at 10:50 a.m.