I am a current pre-specialty student so I will do my best to respond. I had a 1310/5.0 GRE (the old GRE) with 3.5 GPA. Of course, I don't sit in on the admissions decisions so this is based on my experience of the program and chatting with other students. (You'll soon stop obsessing over these numbers when your first test comes around! You'll be too busy to care who was summa cum laude in undergrad!) As I see it there are two factors to consider:
1. You are not only applying to the generalist (RN) nursing program but also the specialty (ACNP, FNP, NMW, etc.) program. Therefore, your application is reviewed twice in a sense--once to determine if you meet the general expectations to enter the pre-specialty component and then again to determine if you meet the expectations for your selected specialty. The specialties' selectivities vary somewhat so it is hard to tell you specifically what the numbers mean for you. I know admitted students whose GRE scores were in your range; I don't know about the GPA, but I would not be terribly worried about yours. Generally, I would say that those numbers are certainly not prohibitive but...
2. They probably need to be backed up by a well-rounded application. Unlike applying from high school to undergraduate programs, your application should show that you are well-suited for advanced practice in your chosen area, that you have some experience (volunteer, patient care assistant, related employment) where you have "tested" your desire to enter the profession, and a good grasp of what nursing involves (since you are not yet a nurse). Being able to provide personal examples in your essays will strengthen them, and your reason for entering nursing should be more nuanced than "I love to help people." Police officers, firefighters, social workers, counselors, and other professions help people; what is it about nursing that calls you to the profession? Also, evidence that you are a good writer will strengthen your application; we do write papers, and they are expected to be of good quality. Good writing on the application can leave the reader with a favorable impression of you that can compensate for other weaknesses in the application. (And we ALL had a weak point in our applications! Don't worry!)
Finally, let me encourage you. I have a friend who is very smart who did not get in initially, but she was admitted off the waiting list and is doing very well in the advanced practice portion after completing her pre-specialty year. She expressed continued interest after being placed on the waiting list and periodically (I'd say maybe monthly.) checked in with admissions to let them know of her interest should spaces open up. This doesn't mean that checking in is a guaranteed way to get a spot off the waiting list, but admission officers may look kindly on a student who is professional, expresses interest in Vanderbilt, and persists through the challenge of the waiting list when they consider offering spots that open up.
If Vanderbilt does not work out for you this year, I think it is perfectly acceptable to request feedback on ways you can strengthen your application. Not only will you get the inside track, it shows that you are committed and seek feedback for improvement--a great professional behavior! Remember too that there are many ways of entering nursing. A second-degree BSN may be a good fit and a way to show your abilities in nursing by a strong performance in the BSN. Keep your options open, but be persistent if Vanderbilt's program is your goal. It can be done!