If the exchange markets stay open then the price will likely continue to grow, but if they get shut down (which is likely to happen in this world we live in), then the prices will plummet.
They will plummet at least momentarily due to decrease in fungibility, but BTCs will continue to be traded irrespective of whether there are bitcoin exchanges around or not. So, lack of exchanges won't be the end of bitcoin, or necessarily place any fundamental cap on the value of BTC.
Lack of exchanges would make it a lot harder to determine the exchange value of bitcoins against fiat currencies, however.
Joe's Web Shack accepts Bitcoins for hosting services. He wants 3 BTC for a service comparable to $100 USD. Given the current value of the BTC, it's a good deal.
2 days later, exchanges are shutdown and people have very few options of converting BTC into USD. Joe's Web Shack no longer accepts BTC since their value is lost and there's no way to pay the bills with BTCs.
Govt shuts down some BTC exchanges -> BTC value plummets -> Companies accepting them either overprice their goods for BTC or stop taking them -> BTCs are now worthless. It won't be a momentary collapse, it's naive to think so.
It's a new currency, it will have to fight to survive.
If mighty US gov. seriously tries to kill the Bitcoin, I say it's a good thing for two reasons: 1: They will fail and look stupid which will probably refrain many other governments from trying (ok, governments in general might not be known for learning from others mistakes, but still...) 2: The Bitcoin, surviving a attack from the worlds most powerful government, will look a lot more solid and reliable...
A government can never stop bitcoins entirely, for that they would need to seize all hdd:s and servers in the whole world that store bitcoins. That, of course, will never happen. What they
can do is banning all the the sites that exchange bitcoins or accept it for payments like mentioned. That is, those based
in the country of the government in question, in this case US. If most other countries act like US, we will end up exchanging bitcoins in the same countries we today use for "anonymous" offshore-banking and webhosting: Isles of man, Panama, Cayman Islands, Channel islands etc. For the user, the physical location doesn't really matter so this will not change much. There will always be countries where it's legal. It will be less attractive with less places that accepts it, sure, but far from useless. But that's kind of a worst case scenario, the bitcoin will probably be legal in many countries. Not that the governments want it but many of us lives in democracies, and the
people will want it. But gov'ts will of course use scare-tactics and propaganda to change the general opinion. I'm seeing them using three arguments: 1: the It's-mostly-used-for-illegal-activities-arguments, 2: The deflation argument, and 3: The-governmen's-lack-of-control-arguments (although that is the beauty of it for many people). So let's see if the people buys it...