The 4 year nursing degree will do. You do not need to major in science to go to med school. What I meant in my previous post was that 4 year nursing programs usually offer a BSN (Bachelors in science in nursing). What you should do is talk to the admissions officials for the nursing program you are applying to and ask what the specific biology, chemistry, and physics and organic chemistry requirements are to get into their nursing program. Then ask if those nursing school prerequisite science courses are the same that the premeds take. If they are not then see if you can take the premed chemistry, o-chem., physics, and biology courses to satisfy the nursing school prerequisites. That way you are killing two birds with one stone (Taking care of the nursing school requirements as well as the premed requirements at the same time).
At school, the pre-nursing students take a series of nursing courses similar to premeds, but they are watered down and not as hard as the science courses the premeds are taking. In other words the pre-nursing science courses have a lower rigor and are less difficult than the pre-med science courses. For example, at my school the general chemistry that pre-nursing or nursing students take is called Chem3A and is only a 1 semester survey of general chemistry. As a premed, the general chemistry I had to take was called Chem1A for the first semester and Chem 1B for the second semester, which are way more indepth and difficult than what nurses take. Premed General Chemistry is spread out over 1 year so you take one sequence per semester as opposed to the nursing chemistry, which is only 1 semester long and more of a survey of the course.