Yes, the government can stop bitcoin, I am sure they can. But the problem is they need to shut down the internet connection in all of the world because bitcoin is connected with the internet. Although the government ban bitcoin, I am sure people will search another way to use bitcoin if they think bitcoin can bring more benefit to them. But I don't think that the government will stop bitcoin and I think they are thinking about what they can do with bitcoin
They don't need to shut down the Internet
In fact, they don't even need to ban Bitcoin directly as cracking down on major exchanges will suffice for bringing it down. It won't kill Bitcoin, not in the least, but that will make its use not worth it. Strictly speaking, Bitcoin is not a great threat to governments anyway (I mean major ones), so they don't need to do anything yet. But we can already assess the effect of such intervention by an example of ZCash. It was banned on a couple of important exchanges and now it is of no interest to anyone