Sure, but China has already restricted it and if the US does as well that would be the two biggest markets. Bitcoin will probably continue to exist because it can't be completely removed given its architecture, but the US can make it very difficult for users to trade it or purchase it. It is already almost impossible to mine it. If you look at Bittrex, they just stopped allowing US citizens to use their platform. Without the US market, they folded.
There is nothing that can be done legally to stop people from holding or exchanging Bitcoin for goods or services, but they can do lots of things to make it difficult to transact. They can also put pressure on other governments to overregulate it too.
There is a big lawsuit going on now with Coinbase. The SEC charged them with operating an unregistered securities exchange. Coinbase is arguing that crypto is not the same as securities and, therefore, the SEC has no jurisdiction over the Coinbase operation. Coinbase has asked a judge to dismiss the case. We are waiting to hear the judge's ruling on that. If the judge agrees with Coinbase, it will limit the government's ability to regulate the crypto exchanges to some degree. But there is still the IRS and a few other agencies that could get involved. The fact is though, these exchanges and cryptocurrencies have been around for a while. Why is the SEC suing now? I believe it is because there is a quiet war on crypto and this is all just part of it. Cryptocurrencies make it very difficult for the IRS to tax income because they cannot trace wallet transactions without a warrant, but getting a warrant requires probably cause which is hard to establish if the identities of the parties or the nature of the transactions cannot be determined.