Well the degree you get doesn't really matter. I've flown with Forestry majors, Liberal Arts graduates and Geology majors... Then, of course, I've flown with captains that were doctors, lawyers and PhD's as well. Almost 100% of new hires at the majors have **at least** a four-year degree.
Personally, I think a college degree is a reasonable requirement for employment as a pilot. No matter what the flight schools tell you, this is an ultra-competitive career. An airline might hire 800 pilots in a brisk year, but there are probably 12,000-15,000 applications from qualified applicants on file for the 800 or so that are hired.
New hire ground school and any subsequent professional aviation training you do during your career is not like going down to the local FBO for private pilot ground school.
You need to have the ability to budget your time between aircraft systems, learning aircraft-specific manuevers for the simulator and finding a little time for an occasional meal. I've got about 60 pages of notes and a stack of flashcards 4-inches thick on the MD-88 and MD-90 systems and limitations.
If you can complete a four-year degree, the same study habits you used to earn that degree are absolutely fundamental skills that you'll need when you're in 757/767 ground school.
Like people said earlier, airline ground school (which is something everyone has to go through until they retire) is like trying to take a small sip from a fire hose of knowledge at full blast.
Unfortunately, it's more cost effective to have a fast-paced, high intensity training atmosphere for pilots and giving those that "fall through the cracks" extra training, because every minute you're not flying passengers, you're costing the corporation money.
Hope I helped!
Delta MD-90 FO