To date, government officials, defense organizations and the DHS have all been working on disparate missions when it comes to cybersecurity. Getting everyone working together can be a challenge, he said.

The mission of the intelligence community, for instance, is to intercept an attack using the cyber infrastructure; the DHS is supposed to protect critical infrastructure; the Department of Defense has defense-and-attack authority; and the White House has coordination authority. The question that will need to be asked is whether "all of the right players are at the table or if there is a need to add more," O'Brien said.

Also key: figuring out how to ensure that the private sector is "holding up [its] end of the deal" when it comes to the critical infrastructure in private hands, he said.

Enrique Salem, the CEO of Symantec Corp. , said in a statement that the decision to re-establish a strong White House role for cybersecurity is "gratifying." The last executive to have a cybersecurity role in the executive offices of the president was Richard Clarke, who was special advisor on cybersecurity to President George W. Bush when he retired in 2003.

In the six years since, cyber security oversight and involvement has moved from the White House to other government agencies, even as cyber attacks have grown to the point where they are now a "full-blown threat to national security and commerce," Salem said.