CISPA safely passed the House on a bipartisan vote last year despite the veto threat.
The House Rules Committee will decide the rule for CISPA on Tuesday afternoon.
The bill is aimed at making it easier for government and industry to share data about malicious source code and other cyber threats with each other so firms can take steps to thwart a cyberattack.
Last week the House Intelligence panel adopted a set of amendments into the bill that were intended to allay the concerns of privacy advocates and the White House. Rogers and Ruppersberger backed those amendments and said they were aimed at addressing misperceptions about their bill.
Following the panel's markup, the White House lauded Rogers and Ruppersberger for making a "good faith" effort to address their privacy concerns with CISPA, but said the amendments didn't go far enough to address outstanding "fundamental concerns" it has with the bill.
The White House has declined to comment on whether it will issue another veto threat against the bill this year, but has noted that it only issues statements of policy when bills are ready to be considered on the floor.
Ruppersberger said the aim is to get to conference with the Senate on an cyber information-sharing measure, which is when the administration's concerns can be ironed out.
"I think the administration's strategy, and they speak for themselves, is that they think it gives them more leverage to get things they want [in the Senate]," he said. "We're just trying to get the bill moving."
The Maryland Democrat said the bill is needed to address the rising threat of cyberattacks against the country.
"The most important thing, we're being attacked on a regular basis. In today's climate, this is really important, more than ever, to move forward—to get it to the Senate [and] work it through," he said.