BTC will be around but a fluid market for BTCUSD or BTCEUR -- ie. a plentiful amount of people interested in buying or selling bitcoin for other currencies -- won't necessarily be.
Or maybe people would simply lose their interest in to bitcoins, or start using something else. Maybe Google will invent their own bitcoin, and everyone starts using that. Or maybe something else happens.
When the USG starts shutting down the exchanges, which will happen any minute now, Bitcoin will go to zero and stay there. Everyone who thought their BTC was worth USG will want out - and find that the doors are now locked. The BTC price won't even be epsilon. It'll be zero.
The monetary design of Bitcoin is sound. The political design, not so.
The USG has been successful killing payment companies before (eg e-gold, epassporte, neteller), but those were of course centralized systems. Bitcoin is decentralized, which is why its supporters believe that it is here to stay regardless of the actions of any particular government.
The US dollar is a centralized system. US financial regulation is in effect worldwide (except now Iran, I guess). If you have a decentralized system dependent on a centralized one, it's a centralized system.
Bitcoin is not dependent on the USD for its operations, just for its value. The day after MtGox (for instance) is indicted, everyone will be selling and no one will be buying. Also, all payment processors everywhere will cut off all Bitcoin exchanges everywhere.
(Everywhere excluding Iran, I guess. Is Bitcoin big in Iran?)
I wouldn't say 'big' exactly, but the participation is non-zero: http://blockchain.info/nodes-globe?series=48hrs
But what about your neighbor Bob's place? You buy him dinner, and the next day a string of bits comes your way via Tor (or somesuch.) There is no need to utter the word "Bitcoin" during said dinner. A wink, a nudge, etc. will suffice. The next day, Bob does the same with his neighbor Charlie. And so on.
And, naturally, if Bob were a traitor, he could rat you out to the Gestapo. But he could just as easily rat you out for [insert extremely popular but highly-illegal-in-the-USA activity here.] No digital cocaine required - the analog kind will do. And if you haven't any under your bed, Bob will helpfully leave a kilo in your toilet tank.
Most people have already had plenty of practice exchanging highly-illegal strings of bits. Now they will just need to learn to give each other "free" stuff as well.
Bitcoin hasn't reached the critical mass needed for this kind of thing, but there is no reason why it could not.
Consider hawala (http://en.wikipedia.org/wiki/Hawala) which is doing quite well despite draconian bans. On which currencies do hawala transactions depend? All of them and none of them.