As I understand it, if the US Govt chose to entirely eradicate bitcoin worldwide the most likely way would be through a 51% attack (please correct me if some other software-based attack might be more effective).
It wouldn't completely eradicate Bitcoin though. It would just shake people's confidence in it and require some very, very ugly solutions.
Mining pools could sign their blocks and could agree not to build onto a block that wasn't signed. Clients could prefer signed blocks to unsigned blocks in reorganizations. One or more distributed, high-speed checkpointing systems run by trusted individuals could be set up. Path dependency could be added to the "longest chain wins" algorithm. The mining algorithm could be changed, forcing the attacker to start over from scratch.