If you mean cyber bullying, no. If you mean hacking attempts against the government and its umbrella of corporations, then yes. It all depends. Online a myriad of things can happen, and who's to say what should or shouldn't be defended against. The president? What can he do about low-level bullying on the internet? That stuff happens in life regardless of the medium. Hacking attempts on a large scale, now that's an entirely different story, but I'm not sure that's what was being asked, truly.
In the US, there are three branches of government. Obama is in the executive branch, which is only one of the three. To effectively deal with cyber-attacks/crime we need dynamic laws, regulations and solutions.
Cyber warfare is not battle in the traditional sense. We are not sending out artillery and soldiers to kill and/or die. Therefore, the defense against malicious online activity should not be conducted by the military. The duty of passing regulations with oversight when creating a line of defense in this situation would fall to the congress.
Our online freedoms can be dramatically threatened if we were to allow a single ruler such as the President of The United States unchecked ability to pass orders without any opposition. They would in essence be able to take over a major form of communication and manipulate it. It is a very dangerous step to allow such a strong action to take place.
Some issues are below the President and protecting from cyber attacks falls much lower on the chain of command. He is not in charge of computer defense he doesn't make the duty roster at any military command leave him to big decisions and do not bother him with petty things that should be handled much lower.
While there is a need to protect the country from cyber attacks, an order to protect us from them is more useful when issued from inside the military structure. If the president issues the order, the entire military is bound by it, and does not have the ability to countermand it or alter it when necessary. This is good in some instances, but not in this one, because the nature of the threat is evolving and will continue to evolve. Thus, the order should come from as far down the chain as possible, and still cover all necessary segments of the military (for example, would this be an operation carried out by the Air Force? Then in should be handled entirely within the Air Force. Would there be units in all branches to prevent such an attack? Then perhaps the Chairman of the Joint Chiefs of Staff would have to issue the order, but I would avoid this if possible).