Difficulty in getting a volunteer position at a hospital all depends on were you are from. For instance, if there is a hospital close to your school, then it is pretty probable that getting a position will be difficult. When I started my freshmen year I checked out volunteer opportunities at the hospital a week after classes started and they said they were not accepting anymore applications. I was lucky and joined a school "club" were I interviewed for a special group within the club that had a standing arrangement within the hospital to send volunteers. But it was a long process and about 200 students put in applications for 10 spots. Because this group only went in once every two weeks, 5 one week, five the next, I also volunteered at a soup kitchen once a week. The next year I was able to get in to the program I wanted a volunteered in the peds ward for about 3 hours a week.
20 hours of volunteer work a week is a little unrealistic. I'm sure people do it, but it is not necessary. I'm sure adcoms don't expect this much. They want well-rounded people, so in my oppinion that means people who also have their "own" life, and so things that make them happy.... like "climbing" for me. You have to remember, if you are science major especially, that alot of your week is going to be spent in class and studying. Add on top of that a few hours of volunteer work and other extracurriculars... like committees and things, and a few hours for you self, and you have a pretty packed week.
Only you know yourself and how much you can handle. But above all don't let you courses go to the way side, they are most important!
Good luck to you, and remember there are other places to volunteer besides a hospital if you a one of the unlucky ones that just doesn't get a position this year. Try Big Brothers or Big sisters. Or a children's literacy program. This are great services, and they give you a great feeling they you have really helped someone out.