| nypd0, it isn't so much that med/grad schools look at quantity as at quality. And the way it works, you're not going to be handed a lot of responsibility or independence in a lab when you first start. You have to earn it by showing your reliable and can handle it. Ideally you then are given more tasks over time, sometimes you have to switch labs if they aren't going to give you more to do but your experience and references will convince another lab to take you on. But the point is the process takes time, and an earlier start gets you farther along.
I suggest you take some time and look on this forum for posts by molliebatmit. She was a MIT student who ended up getting quite significant experience both at her college and thru summer work, and is now in a PhD program at Harvard. She also was a blogger for the MIT admissions department and you can find her blog with google. Spend a few hours reading thru her posts (there's lots of them!) because quite a lot of them comment on how she found jobs, how she progressed to more responsibility, the work ethic she had, and the differences she thought it made when she was interviewing for grad schoool (esp. compared to grads from many large publics like the UCs). | 
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