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.
First world or third world, governments hate letting go off power. Controlling the money supply is one way of exercising power and they would hate to surrender it. They would always view parallel currencies, including bitcoin, as rivals.
I think instead of waging a war, they would do it silently by stealing the technology behind block chain, using it to duplicate their own currency and then ban any other crypt currency, at least that's what I would do if i was a mean evil corporation controlling everything portraying that the power is in the people lying by the idea of democracy.