Rockefeller is a co-sponsor of a bill from Sens. Joe Lieberman (I-Conn.) and Susan Collins (R-Maine) that would empower the Homeland Security Department to set minimum cybersecurity standards for critical infrastructure, such as electrical grids, banks or gas pipelines.
Supporters, including the White House, argue the standards would help to prevent a catastrophic cyberattack that could cost thousands of lives.
But Sen. John McCain (R-Ariz.) and other Republicans argue the standards are unnecessary and would impose an unreasonable burden on companies.
GOP House leaders have indicated they will not allow a floor vote on any legislation that creates new cybersecurity regulations.
The House passed its own cybersecurity bill, the Cyber Intelligence Sharing and Protection Act (CISPA), last month. The bill focuses only on encouraging companies to voluntarily share information about cyber attacks and includes no mandates.
The White House has threatened to veto CISPA, citing the lack of critical infrastructure mandates and weak privacy protections.
--Andrew Feinberg contributed