16,946,489 terrahashes per second right now for the BTC network. According to some website I found you can get an ASIC that does 4.73 Terrahashes for $500. That means you'd need 17638182 TH/s at least to get 51% hashpower. That means you'd have to buy 3,729,003 of those $500 miners which would cost $1,864,501,313.80. Let's double that and call it 3.6 billion for facilities and energy costs. So yes, totally possible for a government to create a cluster with 51% of network power if they chose to. I imagine there would be pushback against spending billions to destroy people'a assets though.
Also in such a situation, consensus could be reached easily on doing a hard fork. Government's effort would go waste on the original one. They can repeat, but it will take some time, and the hard fork can happen again, until govt gives up.
A better approach by any government could be to declare it as illegal (just like drugs). By doing so, they can't eliminate it, but just curtail demand.
They could certainly cause a lot of trouble, but rather than continuously hard forking I bet people would just add hashing power to the network like crazy. It's basically the government vs everyone in the world. If the value of BTC was threatened, I'm sure a lot of hash power could get added into the network. Can the US government outspend and outpace everyone else in the world teamed up against them? It would be challenging logistically for sure, even if you had the money.
Do you think miners can switch faster to the hardfork than the government? The government can just redirect their entire mining pool at once to a new hardfork wheras miners are independent and convincing them to switch will take time.
also worst damage such a government could do would be to double-spend some coins. That is if the 51% is somehow undetected and that the rest of the bitcoin community doesn't fork the chain upon detecting such an attack.
