This isn't a question about technology; as much as the geeks love to obsess over it. Technology is just one part. Non-technology attacks are simply much more powerful. E.g. "Anyone caught using Bitcoin will be executed on the spot by large caliber fire from attack helicopters flying far enough away that you can't see or hear them targeting you", and suddenly Bitcoin is only some obscure and irrelevant thing— even outlaws have no use for outlaw 'money'. There is no question of _ability_ to suppress it, only a question of sufficient motivation.
And motivation is where it comes up short. Bitcoin is just another thing people can barter. Not different from beanie babies or lumps of coal, and it shouldn't be legally or politically different. This whole weird concept of something being unlawful until proven otherwise must be some kind of crazy fallout from the drug and copyright wars, and I fear that thinking will greatly harm society in the long run.
If Bitcoin turns out to be an efficient 'money' then sane and efficient governments should support it: because a more efficient money will make everyone more prosperous. Some people love to feel all counter-culture and subversive with their hobbies, but as disruptive a technology Bitcoin is it's just not politically disruptive. Most of the few establishment risks that go along with Bitcoin apply doubly to cash, the others apply to other valuable commodities that goverments can't just create out of thin air. The motivation to attack just isn't there.