hedge your bets - if your on scholarship and up to the work, dual in comp sci and your engineering of choice.
I just got my undergrad done in August 2010, BS in Chemistry & Microbiology. At the time of this post, I have applied to 300ish jobs, had 9 interviews and 0 offers.
I am now doing volunteer work for the research lab my fiance works for, writing pattern matching programs for bioinformatics.
Getting back on topic, the degree you get will be meaningless after your 1st job and 90% of the material taught in college is of limited practicality. The degree is a gateway to the 1st entry level job. Best thing to do regardless of your major is to network if your worried about job security. Do volunteer (or paid if they can afford it) research and internships the build up a practical resume. If your full of win, an internship can lead to a job right out of college.
The reason I suggest the engineering/comp sci, is the job market and salary for engineers seems to be better than most of the other options and consistent regardless of economy; the comp science degree makes you very market-able and puts on your resume that you can program.
The suggestion I made is what I would had done if I could, change my degree from Chemistry & Microbiology to Biomed Eng & Comp Sci.
Best of luck!