Well, right now you are a definite rejection because of your scores...but not forever
Basically, what even pulled up your score to 19 was the verbal part, since your science scores were very weak. There is hope however, and lots of it. The firt thing I would encourage you to do is to look at your knowledge realistically. It is a natural human tendency to "dance around" things we feel bad about. You need to look at yourself realistically as an applicant:
1) Are you simply a poor test taker? If so, you should have already been aware of it in college, because people do not suddenly become poor test takers, after 4 years of college.
2) Is it perhaps just "freaking out" because of the length of the exam or thinking that "so much is at stake"...? If this is the case, then doing practice tests until you retch at the simple sight of another one may be the answer. It is just like "desensitizing" yourself.
3)You mention you went to an Ivy league University. What was your major? It is hard to conceive that if you majored in one of the sciences, an Ivy league school left you so ill prepared to take the MCAT. Whereas, if you major was, let's say Political Sciences, then it would be more understandeable (although I would expect your verbal score to be higher, in this case). In this case, I would take a few more advanced science classes before retrying the MCAT (which you are going to have to do).
4)Is English your first language? If not, that may be the area that needs improvement.
5)Are you going into medicine having a "knack" for science, or science was always hard for you, but you want to get into medicine because of other reasons such as: desire to help others, prestige, money, family wishes, don't know what else to do and don't want to be a trader...etc. If science was always a stumbling block along the way, then LOTS of science put together (such as on the MCAT) is not going to be easy. If this is the case, I think a recosnidering of career plans would be in order.
6)Try to find someone to quiz you on subjects that appear on the MCAT. Sometimes we really do not know something that we seem to think we do. When someone asks you about it, your gaps in knowledge can be made apparent and then you can focus your efforts on these areas. One of the time honored traditions in med school are study groups, as you will find out, so if your problem is in not been a good evaluator of your own knowledge, try to prepare for the next MCAT with a couple of other people (not exclusively, of course) but your study groupd can meet once or twice a week.
7) If test taking gives you hyperventilation and panic attacks, seek professional help. If this is your case, it is really tough trying to score well on a test while you are concentrating on your heart beat going ape. Since med school will be an unending marathon of tests (aaaaaargh), better take care of the problem now.
Don't despair and again, don't make excuses for yourself, no matter how hard it hurts. It is only by assessing your strengths and weakness objectively that you will be able to overcome this hurdle. If you take the MCAT again and do well, there is no reason why you should not get an acceptance somewhere (at this point, your chances for a top tier school are gone, but not your chances of getting into less prestigious programs).
Good luck and let us know how it is going for you!