I studied in Aerospace Engineering and now work in industry. I do mostly research and development work, but on a variety of aircraft and spacecraft. I had the same kind of question when I first decided what to study so I'm happy to give you my perspective!
I currently work with people of all kinds of majors - civil, mechanical, and aerospace. There are a lot of similarities in those areas when it comes to aerospace work. You would be able to find a place in the industry regardless of major you do when you learn the engineering behind it.
Mechanical Engineering tends to give you a broad perspective of engineering and gives you opportunities in many areas - aerospace, cars, construction, etc. Some people think that Aerospace can be limiting, but like mechanical there is application of the major in other areas too. What is most important is getting a good foundation in the engineering background.
A major in mechanical with a minor or emphasis in aerospace would definitely work and I would recommend it to give you some exposure to hands on aerospace type of work and background for your first job. If that's not an option, some schools have clubs and hands on programs that all majors can join to participate in projects and lessons in the industry their interested in, so I would definitely take advantage of that. Internships and summer programs are another good way to give yourself exposure to the industry.
It is most important to find something that you like in a good program. If you already know you want to work in aerospace, going into that major would give you the opportunities to start studying right away in the area that you enjoy. You may find that you enjoy your classes more when they relate structures or aerodynamics problems to a shuttle vehicle rather than a car.
But if you found good a university or a program that you like that does not offer it or only has the minor/emphasis, you can still be successful working in aerospace.
Good luck! Nikki