If they defrauded their customers, were subject to a serious heist or were blatantly ignoring the four pillars of a good compliance program they will be shut down. None of those are things we can easily predict however.
Coinbase is only licensed as a money transmitter at the federal level. In order to legally provide money transmission services in any state, it must also acquire a license in that state. (Under international and federal legal conventions, digital services performed by software are treated as rendered in the customer's location, so Coinbase would need a money transmitter license in each state in which it wants to do business.)
It is registered as a Money Services Business with FinCEN, which is a signal that its officers, directors and investors are aware that state licenses are required by law for the business they are in. That's different than having a license, however. In the United States, there's no such thing as a federal money transmission license unfortunately.