Having gone through an Aerospace Engineering degree program, my experience and advice may help you out.
I decided on studying Aerospace Engineering because I thought engineering would fit my talents in building things, intuition for solving physical problems, and performance in math classes. I also thought it would lead more directly to a career.
However, even before my freshman year, I read some popular science books on physics. I also realized that I really had a passion for physics. But, I had made the decision to get this degree in Aerospace Engineering, so I carried that through without thinking much about it. I figured I would figure out the rest after finishing the degree.
I graduated in 4 years, and realized that my passion for physics didn't ever go away, and that I had to make a u-turn. I won't go into this any more here, but essentially I am still figuring out my career. Take this to heart--you might change your mind. At the same time, if you are more excited by sitting in the classroom or learning from a textbook than you are by working in a group to build something real, then I suggest switching to math or physics (as I wish I had done). However if you like to build stuff more than you like theory, stick to the engineering side.
Ok, with that in mind, here's my advice to you.
First of all, your graduation date (i.e. the time to degree) is secondary to quality of learning, and above all else, connections and work experience in the field. For example, get involved with a hands-on project/competition teams as soon as possible. Get involved with any local engineering companies you can and start racking up real world experience, and find mentors. Find older engineers you can follow around and learn from. Try to spend time working for professors doing research, as well. See if you like research. Try doing some student teaching--be a volunteer tutor or if you can, be a paid undergraduate "Learning Assistant." Some programs have this as an option.
What you'll find is that teaching others will advance your own knowledge and ability to learn; at the same time this will develop both your ability to lead, ability to communicate, and confidence.
You'll find that getting work experience will connect your fast-paced theoretical knowledge to the real world to make it relevant. The concepts in the book apply to real things that you can touch and test.
You'll find that doing engineering club projects (for example, RC aircraft projects or bridge building) are fun and keep you socially connected to your area of study.
So to condense that down:
1. Quality over quantity in your education. Really MASTER your course material. This will pay off if you want a more academic career later on.
2. Do some student teaching or tutoring ASAP. Tutor for money or for free, either way is worth your time. You might even meet your future wife that way. :) Also, if you enjoy teaching more than research or studying, then make that your career.
3. Do a project related to your studies, either a mandatory one through school or for fun. If this inspires you more than teaching or research, be an engineer.
4. Get research experience at some point, and get work experience at a company (not at the same time!) If pure research is most inspiring to you, go to grad school and become a scientist.
Another bit of advice: Try to find good mentors, i.e. advisers that are wise and willing to share their experiences with you openly. A single good adviser, in any field of study or work, may inspire your entire career. This takes work on your part though--you have to try working for many different people until you find ones that inspire you. This is why I don't recommend going to a research university for your undergrad--many researchers make poor mentors.
That's a lot of info for now. If you have any responses to that then I can give you more detailed suggestions.
