I guess I can see the point that advocates of the bill have. We will need to do something to protect cyberspace infrastructure as it becomes more and more important in life and allows access to more and more valuable information. I do agree, though, that this bill seems far too broad.
Granting the president power to shut down avenues of information or even private sectors I believe is a step too far. This seems to have the feel of the warrant less wiretaps from the Bush era. As long as there is an "emergency" the president should be able to do anything he need despite those pesky laws.
I think there is definitely historical precedent here with how military action by the whim of the president has developed. It doesn't matter if war is declared because the president can deem it a police action. The Iraq War technically isn't a war. Congress can always pull funding, but Teddy Roosevelt put forth a very effective model on how the president can combat that with his "Great White Navy," and Bush was able to use the same ideas to paralyze congress with regards to the Iraq War.
It's just too easy to twist the terminology or situation every which way to justify extreme action. And having a Czar simply makes it worse. Putting so much responsibility in the hands of one person makes it even more likely power will be abused.
Personally, I think this could be better addressed with a bill containing more explicit restrictions as well as creating and Independent Regulatory Agency instead of appointing a Czar. That way, there would be a board of people that would be making such decisions, which makes it harder for one person or agenda to easily seize power. Additionally, the board members could not be dismissed at the whim of the president or unelected(though congress could alter the agency via a new law), granting a good degree of autonomy. And, of course, the agency's actions would be subject to judicial review.