How much would it cost for a government to undermine Bitcoins?
As I suggested in my Bitcoin master thesis, a 51% attack would cost in a bulk part of about 7 million dollars to execute. The figure will change depending on the technology used, the current difficulty and so forth. This option would make Bitcoin or any other Bitcoin-like currency useless.

However, if the USA goverment was to crack down on Bitcoin as a terrorist activity, it could detain any Bitcoin developer in the country indefinitely, which would probably be cheaper. This option would most likely generate a lot of backlash from the community, and could encourage other programmers to take over the project.