I doubt the general public would approve of a budget for buying thousands and thousands of AMD video cards. I'm not so sure that would get past any budget hearing.
We already let them get away with $100,000+ expenditures for "toilet seats." They would just bundle the cost of the cards or whatever in with something else and then call it something bullshitty. That's assuming that they even use cards, with their resources, I'm sure they have something that could be made much more efficient and scaled up as big as they need.
The money will definitely be available to them one way or another.
By the time the government has to take this extreme of measures to control bitcoin, it will already be so huge that it will be uncontrollable. For this to happen, the government would have to allocate all of it's computing powers RIGHT NOW in order to take down bitcoin, but with the growth in terrahashes that is now being seen, soon it will be impossible instead of just extremely extremely unlikely
I agree with this statement, the government would probably ignore bitcoin until it stopped being a niche, and by then it would probably be too late to do anything about it. I believe that hash rate (and difficulty by that token) will only go up from here, and at greater rates than anything we have seen thus-far.
I think that if the government decided to take over the majority today though, they wouldn't even break a sweat. They'd just call up China and be like "Hey, want us to owe you some more money?"
Here is some math someone can do if you are as curious as me, how much money would it take to double the network's current Ghash rate using standard mining rigs. By this, I am wondering how much money it would cost you to build a 1 Ghash rig (or 2 or whatever setup is most cost efficient per Ghash) multiplied by the current hash rate. For example, if it cost the government $1000 to produce 1 Ghash then today they would need between $11,000,000 and $12,000,000 to take a majority. That's about how much money the government uses to wipe its ass after a morning shit. So if something made them want to take bitcoin down now, I think it would be very doable. Of course, by the time the government does see bitcoin as a serious "threat" and jumps on the bitcoin mining boat, they will likely be toooo late, just like most of us that are still slumming around in the newbie section.
Keep in mind that the government would more than likely have a much more efficient method of hashing. (massive FPGA arrays?)
Again, I am fairly new to bitconomics so these posts of mine are just me thinking out loud.