I am focusing on working with Deaf patients, so I'll make a little argument against the previous comments of spanish being more important. Of course knowing Spanish will cover more patients, but do not look over the impact you can have. If you are fluent in sign language, depending on your location, I can tell you in all honesty that you will definitely be the only doctor who is in your town, most likely in your county, and in your state you could only count on your hand how many are fluent (and that is an overestimation). This is because although there are great stories about deaf individuals getting through medical school, it is almost an anomaly. When I interview at places, the interviewer will usually say "oh, about 12 years ago we had a deaf student here", insinuating that this is a great success. Imagine someone saying "oh 12 years ago we had a person who was a native spanish speaker".
I talk with a lot of Deaf people and they say, "just tell me where you are going to set up your practice and I will move there". There is such a desperate need. If a deaf person shows up to the ER in a community hospital and there is no interpretor, they are screwed (unless there is some family member who can translate), but with spanish there is a higher likelihood that someone in the hospital (doc, nurses, staff, visitors) can speak the language, and help (although this kind of "is there an interpretor in the house?" format is deplorable).
So I think it is something that if you want to feel like you are making a huge dent in a health care system that often makes you feel like you could disappear and no patients would notice, ASL could be for you. But if you are looking to tap into as many unrepresented patients as possible, spanish may be for you.
Another downside to ASL, it is pretty much only used here. With spanish you can get by in several countries (even still be fluent in many), but with many countries there are different sign languages. But it really does not need to be a judgment call. Try them out, see what works. I tried spanish, even latin (of course not for actually using with anyone) and just couldn't grasp it. But the visual nature of ASL just came easy to me (well not easy, but I didn't mind the struggles that come with learning a language). And I feel in love with deaf culture. Just try it out and see if it works for you, if it does, you will be helping a great deal of people.