A 3.1 would be good enough for DO school. The amount of work you will need to get a B.S. in engineering will be much more than the work required to get into medical school. Assuming you are a bio major, almost all of your classes are not going to count for anything in engineering. In my program (mechanical engineering) the only classes from a bio major that would transfer would be physics I & II, chem I, english I and II, (4) humanities and calc I. One of my classmates had a masters in sports marketing. He took all the same classes I did and only graduated a semester before me.
By the time you graduate with an engineering degree, you could be in your second year of med school. Fixing a poor GPA for med school takes way less time then doing a new four year degree from scratch. Also, I disagree with everyone saying you should go into another health career. If you want to do engineering, do it! I think physicians and engineers take similar approaches to solving problems. Engineer's have to diagnosis problems and create solutions just like physicians, although I would say that the work environment is completely different.