As far as I know given my not so wide knowledge here in the crypto currency community, there no way that the government will be able to trace a certain people if he or she is having a Bitcoin. Because first and foremost, the Bitcoin is a decentralize which also has a peer to peer transactions. Unless you say it yourself to the crowd that you are a Bitcoin user.
That is not true. The fact that bitcoin is decentralied has nothing to do with identification. It's the question where and what type ot traces do you leave when using bitcoin.
If you are registered at one of exchanges you also have to provide your ID and other personal data and on the request exchanges have to provide these data to law enforcement. Also, there are some tools that enable tracing transactions so don't think that you are completely anonimous.