I don't think it's technically possible. For the moment, at least. The government might get some kind of a tool to do so, but as far as I understand, they don't have a way to do so directly. 
Right. They cannot do it directly, but they can catch some people when they are trying to spend some fiat they had earned from the crypto: some governments have a threshold amount for spending in their country. As soon as the amount you are trying to spend legally reaches the threshold amount, they start demanding that you provide some proof of the source of money you are going to spend. This is one way to control it, but there might be lots of others.