Collins emphasized that the bill's supporters are still meeting with critics, led by Sens. John McCain (R-Ariz.) and Kay Bailey Hutchison (R-Texas), who have put forward their own proposal, the SECURE IT Act.
"I think the differences are narrowing, but there's no doubt that there still some pretty significant disagreements," said Collins, who has co-sponsored the Cybersecurity Act, along with Sens. Joe Lieberman (D-Conn.), Jay Rockefeller (D-W.Va.) and Dianne Feinstein (D-Calif.).
"I just think it's irresponsible if we do not pass a bill," Collins said.
The White House and Senate Majority Leader Harry Reid (D-Nev.) are also pushing for the legislation, but some GOP senators are worried the legislation will impose unnecessary burdens on businesses.
The supporters of the bill watered down the regulatory provisions last week, replacing government cybersecurity mandates with incentives to meet voluntary standards, but that does not appear to have been enough to appease all of the critics.
Both Lieberman and Collins said they believe there is still time to reach a deal. But with the Senate set to break for the August recess after this week, supporters will have to work fast to secure the 60 votes they need to approve the bill.
—Jennifer Martinez contributed.