Senators vow to push ahead on cybersecurity, even without compromise

"I'm for taking it to the floor and taking it to the American people, and you have to decide, do you want to protect the people or you're making the perfect the enemy of the good," Mikulski said.

Collins emphasized that the bill's supporters are still meeting with critics, led by Sens. John McCainJohn Sidney McCainSenate's defense authorization would set cyber doctrine Senate Dems hold floor talk-a-thon against latest ObamaCare repeal bill Overnight Defense: Senate passes 0B defense bill | 3,000 US troops heading to Afghanistan | Two more Navy officials fired over ship collisions MORE (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 RockefellerJay RockefellerOvernight Tech: Trump nominates Dem to FCC | Facebook pulls suspected baseball gunman's pages | Uber board member resigns after sexist comment Trump nominates former FCC Dem for another term Obama to preserve torture report in presidential papers MORE (D-W.Va.) and Dianne FeinsteinDianne Emiel FeinsteinDems call for action against Cassidy-Graham ObamaCare repeal Feinstein pushes back on Trump’s N. Korea policy Feinstein on reelection bid: ‘We will see’ MORE (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 ReidHarry ReidThe Memo: Trump pulls off a stone-cold stunner The Memo: Ending DACA a risky move for Trump Manchin pressed from both sides in reelection fight MORE (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.