I wouldn't say the major is much of a limitation. It just tends to go hand and hand with the ammount of research people have done.
If you're not in engineering or in one of the natural sciences, odds are you
1. have not had a signficant basic science research experience
2. are not well prepared to begin such PhD
3. are not convincing that you want to pursue medical research. THESE are important things.
The perceived rigor of your major is likely important as well. ex. Most people in science are not going to take a business degree from most places seriously. In contrast, I know that there are quite a few math majors in my mstp.
I'm sure there are cases of people who were majoring in (insert about anything here)... discovered bio, chem, biochem etc in their final years and continued on to take a few summer classes and do research for a year or so and then went on to an MD-PhD program.
If you're asking about yourself, you should provide us with some more details about your background and we can give you more specific advice.