Edit: However, I don't think this bill goes around due process: stopping a crime and punishing somebody for the crime are different. Cease and desist orders are tantamount to a police officer yelling "freeze" at a criminal suspect. Due process is given before punishing somebody in the criminal justice system, not before stopping the crime. That doesn't make the bill at all reasonable, though.
Not quite, but close. The officer who says "freeze" to a criminal suspect is an employee of the state and sworn to uphold the law, deputized by a sheriff who is subject to election. There is a check on bad behavior (even if it isn't exercised nearly as much as it should be) and abuses can be punished.
In this bill, the people saying "freeze" are not subject to public review, they are employees of private companies and there is no method of going after or punishment for people who abuse this power. We already have abuses of the DMCA of this nature, this just makes the issue even worse.
Violating a C&D order just means that you wind up in court and have to defend yourself. SOPA will cause your service to be cut and you have no legal recourse.