Casual investors will immediately drop BTC, same with institutional investors, most Bitcoin businesses would close. The only people left on the network in the US would be cypherpunks, criminals, and buyers of illegal services. On a global scale Bitcoin will suffer from a huge crash, easily 90-95%, because if the US would ban BTC, many other countries would follow. If the EU would also ban, it would effectively be a worldwide ban, because most of Bitcoin traffic comes from the West, and the West is very influential, plus eastern countries already don't like BTC and are talking about banning it. Without enough hashpower Bitcoin would be easier to attack, which puts yet another instance of selling pressure on it.
In the end, Bitcoin will not die, because it''s decentralized and it can't be killed, but for most people it would be as good as dead, law-abiding citizens wouldn't want risk dealing with BTC.
Bitcoin can't die but what would be its use if most of the people who are into it right now will stop dealing with it? Virtually, it is going to be dead just like any good product that finds no critical size of a market. Now, using the scenario above, can we then conclude that the "life" of bitcoin is at the fingertips of the government? Though, of course, I don't expect the USA government to do what China did in 2017.