Biomedical Engineering is a very broad discipline, and that's what makes it interesting. It covers many areas such as genetic engineering, molecular/cellular biology, biomechanics, biomaterials, computer simulation of biological processes, prosthetics, etc. Basically you can get into any engineering or science major in college and still find a way to apply what you learn there into biomedical engineering. The first thing is that you need to find out what interests you about the cardiovascular system. Do you want to understand the blood flow pattern in the large blood vessels? You would probably need to have a strong background in fluid mechanics (mechanical engineering) and just the basics of human anatomy. But if you want to understand how the blood cells or cells that form the vessel wall respond to the forces of the blood flow, then you may need to spend more time in molecular and cellular biology. If you are thinking of designing the control system for pacemakers or defibrillators, you may need to know more electrical engineering. And if you want to explore how pharmaceutical drugs affect the cardiovascular system, maybe a chemical engineering background would give you an advantage. All in all, I think you would need to look for chances to talk to working biomedical engineers (not someone who just has a degree in biomedical engineering), and when you're in college, shadow a graduate student or a postdoc in a lab to see if that line of work is what you truly want to pursue (like will you be working with devices, computers, animals, cell cultures, chemical agents, etc.). You don't have to have a degree in biomedical engineering to work as a biomedical engineer. It's more important that you find what you actually enjoy doing.
You have selected an incredibly exciting and growing field, so congratulations! My advice is that since there are very few academic programs that provide combined science & engineering doctoral programs, try to attain some internships in biomedical engineering to get a sense of working in industry. There are some big companies with huge internship programs, such as Boston Scientific, Johnson & Johnson, Medtronic, and there are hundreds of smaller companies (especially in Cambridge, MA) that may have some summer internships here and there. It is important to gain some working experience, because when it comes to engineering, school setting and industry setting can be very different. With a few summers of engineering work experience, you can attend graduate school in cardiovascular physiology and gain the science background. I think combined skills in science & engineering will become more and more valuable as we continue to push biological research and technology. Good luck and please feel free to contact me if you have further questions!