Bitcoins will be hard for them to stop without shutting down the entire internet. Should a government act against bitcoin, it would drive the price through the roof.
The government of first world countries would never want their beloved currency to go to waste. They are already acting against it. They can't fully go through with it, however. It's a decentralized currency. The only possible outlet they have is putting place laws and regulation that make it harder to obtain or trade. NYC bitcoin LBC exchanges have pretty much been banned because you need a license (which is hard to obtain) in order to purchase/trade bitcoin. I wouldn't be surprised if more came.