What type of engineering are you looking for? Manufacturing, ECE, Civil, Aerospace, etc?? My current job title officially states "Associate QA Engineer" but I was a Management Information Systems major. ... although it has more to do with conceptual (data testing) than physical engineering.
Really you should just go for what you like doing the most. I have friends in every major listed above that went simply because they liked doing what they were doing. I also know someone who graduated civil many years ago but ended up never working it (accepted manufacturing and ECE type jobs instead), so even if you can't land a job in your major a strong general engineering background is good.
