That was essentially my situation. I started out majoring in computer science and engineering, and discovered that I had no passion for it. In fact, I hated it. I did, however, discover a passion for philosophy. I completed the program in computer science, but also picked up a degree in philosophy. I was fortunate that my particular area of interest -- cognitive science, including philosophy of mind, artificial intelligence, and psycholinguistics -- was especially strong at MIT.
There may very well be some undergraduates who enroll at MIT with the intention, from the outset, of majoring in something other than science or engineering. For example, MIT's department of economics has historically been as strong as any in the country, and there are advantages to being one of the few undergraduates in an excellent department. (A cross-country teammate of mine majored in economics, graduating in three years with a letter of recommendation from Paul Samuelson.) But if you don't have a really strong aptitude and a pretty high tolerance for science and mathematics, you could be in for some tough times.