Collins: Congress should continue work on cybersecurity despite executive order

"An executive order could send the unintended signal that congressional action is not urgently needed,” she added.

Another draft of the White House's executive order is expected to be circulated among agency officials this week. The draft is still in the early stages and is likely to undergo several more revisions.

There's been chatter that Senate staff continued discussions about moving forward on cybersecurity legislation over the August recess. But it will be tough for a breakthrough to happen on a cyber bill with Congress in session only a limited number of days in September and the election on the horizon.

Sens. Dianne FeinsteinDianne Emiel FeinsteinDHS chief takes heat over Trump furor NSA spying program overcomes key Senate hurdle Democrats will need to explain if they shut government down over illegal immigration MORE (D-Calif.) and Jay RockefellerJohn (Jay) Davison 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.) have both urged the White House to use its executive authority and take action on cybersecurity in lieu of Congress stalling on legislation that would encourage critical infrastructure operators to boost the security of their computer systems and networks.

Lieberman, the chief architect of the Senate cybersecurity bill, is still holding out hope that Congress can work out an agreement on legislation. But if those efforts fail, Lieberman said he also supports President Obama issuing an executive order.

But he notes that there are limitations to what the administration can accomplish in an executive order. Some security experts have noted that the White House cannot offer various incentives to the private sector — such as liability protection for companies in the event of a security breach — in an executive order, as that authority rests with Congress.

“I still hope that Congress will pass cybersecurity legislation. But if Congress cannot get its act together to protect our nation from the real, urgent and growing threat of cyber attack, then the president must do everything he can by executive order," Lieberman said in a statement. "The problem is there are things that must be done by statute."