There is a risk that all the people charge in at the same time and therefore there is a pressure on the entire setup something like a city blackout. The distinction however is that Bitcoin is constructed in such a manner that it corrects itself, gradually by increasing mining difficulty and mining blocks so as not to collapse in its entirety. Heavy network traffic would be the real problem and extremely high fees provided too many people attempt to use it simultaneously. I am personally of the opinion that adoption should be in gradual rates rather than a rush because the system will be able to accommodate such movement.