The hiring process is not pass-fail, it is competitive. Interviewing people is time consuming, expensive, and an all-around pain in the rear. Having to fire someone because you guessed wrong about their capabilities is even worse. That means that if I have two candidates for a job, one of whom has a B.S. from MIT, CMU, Stanford, or the University of Waterloo, and another who has a degree from a school I've never heard of, and everything else is equal, I'm going to be more comfortable hiring the graduate from the impressive school. The good news is that a) there aren't enough graduates from MIT, Stanford, CMU, and U Waterloo to fill all the programming jobs, b) it's really rare for everything else to be equal. The person from MIT may be a jerk, and the person from the unknown college may have published a beautiful open source project.
Some CS/SE programs are better than others. Go to the best one you can. Look particularly for programs with strong internship programs. Work hard at community college and after two years transfer to a four year school with a good program. Some state schools have very good programs. If that just doesn't work out, then yes, you will be at a disadvantage getting your first job. It's not fatal though, you'll just have to find other ways to demonstrate that you're a smart person who get's things done. After your first job or two, where you went to school will be of only passing interest.