Civil disobedience how? You mean like blocking entrances to private property? This isn't like going into a "whites only" restaurant or not sitting at the back of the bus. What do you think people would do?
Why it's not being done on a massive scale right now, I don't know.
Becuse most rational people don't want to be hauled off to jail. Seriously, do you envision millions of Americans forming a "human chain" around abortion clinics? Putting up baricades?