What gives you the most opportunity out of any major is having the drive and ability to use your education beyond its suggested realm. Too many engineers that I know and have lived with are book students, meaning they can recite information they read, but when it comes to actually applying it, they struggle. You see this a lot with bio/chem/pre-med students as well. Proponents of liberal arts majors will argue that their type of education will yield a more "rounded" set of skills and that graduate school will help narrow the field. Dont believe me? Look at the successful alumni of Williams, Amherst, Bates, Colorado College, Pomona, Occidental, etc
One of the most memorable stories I have heard from a pre-med student came from a question on their final exam. The professor asked a question that recited information from the book, then asked why it was wrong, using information they had learned that year. Apparently 1 person in the entire class of 100 students was able to answer it correctly.
If you look at ANY successful person, they all have one intangible attribute in common, they can look outside the box. You do not need to be an engineer nor do you need to be a liberal arts major to do such a thing. What you need is to be able to have the drive and ability to utilize your education beyond its suggest realm. If you can do both of those, there is the possibility to succeed.