First, it is practically impossible to imagine alcohol being banned today. We are moving far enough in the other direction that two states have recently legalized the possession of marijuana for personal use. In such a climate, it is very hard to imagine Prohibition occurring.
That said, if such a law were somehow passed, the response would be largely similar to what happened in the 1920s. There can be little doubt that people would still want alcohol and would still be able to get it. The fact that drugs are easily available through illegal sources shows us that alcohol would be available as well. Criminal gangs would surely rush to fulfill the demand just as they once did. In addition, there is no reason to believe that Americans would be any more likely to stop drinking out of respect for the law. There is already a great deal of suspicion in the US about governmental overreach. People are very jealous of their rights. It is easy to imagine people going out of their way to get alcohol just as a way of showing that they are not willing to allow their rights to be trampled upon.
Broadly speaking, then, there is no reason to believe that Prohibition would work any better today than it did 90 years ago.