Before I dive into my attempt to answer that question, I should mention two similar but much easier questions that are often asked: "Will the government bring down Bitcoin?" and, "Can the government bring down Bitcoin?" Anyone who knows Bitcoin should produce a resounding, "No!" in response to either of those questions. The government will not bring down Bitcoin because it cannot do so.
If you asked a sensible Bitcoin guru what he liked about the cryptocurrency, the fact that it is decentralized would almost certainly be on his list. Decentralization means that no one is really in control of Bitcoin. The peer-to-peer network connects thousands of computers from around the world. In order to shut down the network, the government would have to somehow disable all of these computers or at least prevent them from connecting.
The only way to go about that would be to take out the entire Internet, which is not very reasonable either because the Internet too is very decentralized. It is managed and controlled by all sorts of companies, protocols, organizations, and servers from around the globe. In addition, various vehicles, including satellites, fiber optics, cellular networks, and more, are used to transport information through the Internet. Once again, it would be nearly impossible for the government to eliminate all of this infrastructure. It might be theoretically or technically possible to bring down Bitcoin or even the entire Internet, but I think it is completely legitimate to assume that it will not and cannot happen. There are simply too many people and things working to keep these services alive. No one entity, not even the government, could eliminate all of them.
This brings us to the real question. Will the government try? I think the answer to that question is almost certainly yes, although only time will reveal the extent of their success. In fact, I would argue that the government needs to try. Don't misread that last statement. I don't believe there is any legitimate moral or political reason for lawmakers to go after Bitcoin. Rather, they need to for their own sake, as I will explain.
The government lives off of taxes. There is literally nothing else that enables the government to exist. Who pays the legislators? The taxpayers. Who pays for the fancy architecture of government buildings? The taxpayers. Who pays for government subsidies (which help sustain the government by earning approval and votes from the people)? The taxpayers. I think you get the idea. The government needs tax revenue to survive. If we remember that the government is made up of human beings who depend on it for their income and survival, then we can fairly treat it as a living being that will, as a whole, fight for survival.
Next, we need to note that Bitcoin is a huge threat to tax revenue. Anyone can transfer massive amounts of money on the Bitcoin network without letting the IRS know. Of course, if someone was doing this for the purpose of tax evasion, he would need to be careful not to publicly associate himself with the Bitcoin addresses used for the transaction, but that is certainly possible with minimal effort. Simply put, it would be quite easy to avoid paying taxes when conducting transactions with Bitcoin, and I would be surprised if this was not already happening on a relatively large scale.
Cash too is hard to trace and can be transacted without the IRS's knowledge, but it is not nearly as convenient as Bitcoin. Blockchain.info keeps a list of large Bitcoin transactions, and from it we can see that transactions worth hundreds of thousands of dollars occur all the time. These transactions take just minutes and it is likely that much of this money is sent around the globe. This speed and simplicity is nearly impossible to achieve with cash transactions. This makes the use of Bitcoin a new and significant threat to the government's tax income, forcing legislators to attack Bitcoin or allow their own sustenance to be reduced.
It's hard to know how exactly the government will go about this necessary attack though. Anti-Bitcoin lobbyists should understand that it is probably not worth trying to dismantle the entire Bitcoin network, but there's more than one way to skin a cat. It may be possible for lawmakers to reduce the value of the Bitcoin, and there are several ways that they could try to make this happen.
For starters, they may simply make the use of Bitcoin illegal, hoping to discourage users so much that the Bitcoin hype eventually dwindles to zero. Of course, as we've seen from the Silk Road and other black markets, the Bitcoin economy is completely capable of existing underground. Sure, the Silk Road was taken down, but that does not mean it cannot be revived in an even more secure manner. If Bitcoin was made illegal, its value may fluctuate as fearful users drop out and the economy shifts, but I believe it would continue to exist, alongside tax evasion, and threaten the survival of the government.
Another avenue that the government could take is to try to tax Bitcoin. It would be difficult, but it may be possible to convince users to report their Bitcoin activity and pay the government accordingly. In fact, this probably already occurs to some extent. Large companies like Coinbase probably do report their gains and pay taxes legitimately. The company even reminds users to pay taxes in its user agreement. Until lawmakers devise a more exact plan to deal with Bitcoin, they will simply collect what they can and try to keep evasion at a minimum.
In fact, I think this is the only intervention we should expect for awhile. We need to remember that the Bitcoin economy is still relatively small. The government can still collect more than enough monetary sustenance from traditional transactions, like those conducted at Wal-mart or when an employer pays his employee with a direct deposit. Bitcoin has definitely been growing recently, but it has a long way to go before it will replace the dollar. If that were to happen, the IRS would have a real reason to panic. Some worried users would continue to pay taxes, but I suspect that most would do their best to remain anonymous and keep their hard-earned money. When the dollar becomes obsolete, the government will try to bring down Bitcoin. Unfortunately for those in charge, it will be almost impossible for them to succeed.
As always, there is a minor caveat: I could be wrong. I think it is quite unlikely, but the government could have something clever up its sleeve. For all I know, there's an undercover agent working on the development of Bitcoin-Qt. Heck, maybe the FBI invented Bitcoin and installed some sort of backdoor, hoping that all of the evildoers would pour their assets into the cryptocurrency and then the network could be nuked. Only time will tell.