I was in the same position you were in considering nursing (as a back up) in case the whole med school thing didn't work out. Here's my story, hopefully it can help you.
I was in my senior year of high school and I decided at that time I would actually pursue this dream of becoming a physician. I was aware of how competitive admissions are, so I considered doing a 4-year BSN program in case I didn't make the cut for med school.
Then I realized I was only doing nursing because I was
afraid, afraid of not making it. I didn't want to be a nurse, I wanted to be a doctor. In my circumstance I realized that being afraid of failing was a bad reason to not pursue my dreams.
I contacted my state medical school admissions representative about majoring in nursing as well. He essentially told me the same thing
LizzyM stated, "Nursing course work does fulfill the prerequisites and lacks the depth of the sciences courses necessary for medical school admission."
So I made the choice to major in bio and go all out with my intentions to get into med school. I'm heading into my junior year now and things have been going really all around and they can go well for you too. Also if you are involved in the nursing major you're going to have clinical rotations and other things that could prevent you from committing to involved extracurricular/research, the types of things that medical school admissions committees want to see.
Bottom Line: Become an RN if nursing is your passion, but don't do it just because your afraid of not making it into med school. I knew if I didn't give this my full effort I would look back as a nurse and think of what could have been.
Go for it, do your best and don't look back