Currently, cryptocurrencies are regulated in the US by several institutions: CFTC, SEC, IRS, making it difficult to create overarching regulatory guidelines. In short, yes– Bitcoin can be regulated. In fact, its regulation has already started with the fiat onramps and adherence to strict KYC & AML laws.

Can the government shut down Bitcoin?

No, the U.S. government can't shut down cryptocurrency markets, but they can regulate it.

What will regulation do to Bitcoin?

In the short term, regulations can suppress the trading values of cryptocurrency. But in the long term, it's expected that regulations if done properly, will stabilize the market and make it a safer investment. The SEC is looking at regulating ICOs as securities and is cracking down on fraud.