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 McCainSunday shows preview: Trump sits down with Fox McCain: Tillerson ties to Putin a 'matter of concern' Second Dem calls for probe into Russian election involvement 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 RockefellerLobbying world Overnight Tech: Senators place holds on FCC commissioner Overnight Tech: Senate panel to vote on Dem FCC commissioner MORE (D-W.Va.) and Dianne FeinsteinDianne FeinsteinDem senator seeks more time for 'due diligence' on Sessions nomination Senate sets date for hearings on Sessions's attorney general nomination Senators move to protect 'Dreamers' 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 ReidReid: Comey should be investigated in wake of Russia report Spokesman: NY Times ignored Reid's comments in pre-election story on Russia Senate passes dozens of bills on way out of town 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.