The bill is intended to defend against cyberattacks on the electrical grid, banking, military operations, transportation and others critical infrastructure, The Hill reported.
Obama said he supports the current version of the bill, even though he said it lacks "some of the key provisions of earlier bills," the Capitol Hill publication said.
The bill remains subject to further revision, the report said.
Sen. Jon Kyl, R-Ariz., a negotiator for Republicans, said, "Obviously there's a lot of work to do and not very much time to do it."
Lieberman introduced revisions to the bill last week in an effort to win GOP support, and Majority Leader Harry Reid, D-Nev., said Thursday, "There's still plenty of room for changes."
"Let's have as many amendments as people feel appropriate," he said.
Tech companies Oracle and Cisco have supported the bill, but the U.S. Chamber of Commerce and IBM said they oppose the current version, arguing it would impose too much regulation on businesses.
Celebrity Families of 2014 [PHOTOS]