A letter from a big-name professor might help, but if you don't have a good relationship with the prof. or he/she doesn't really know you very well, it's going to show in your letter. I'd highly recommend requesting letters from those who know you best, who you've taken a lot of classes from, or who at the very least you think could write you a strong letter. A letter that emphasizes your personal strengths and how you manifested them in the professor's class will go much farther than a generic letter that says "x would be well-qualified, I support" but does not offer reasons or insight into your personality.
I've heard of some people even getting letters of recommendation from grad student TAs. While I think that if you did this it would be best to get the professor to sign the letter as well, I think that in general you should be most concerned about how well they know you and can support your application.
One suggestion if you have to get a letter of rec. from professors who do not know you as well is to first of all ask them if they'd be comfortable writing you a strong letter of recommendation, and then asking if they would mind if you have a meeting with them to discuss your goals. Bring a long a copy of your CV, relevant experience, etc and let them know why you want to be a doctor. This will be a big help for them when they are writing your letter, and it will also be impressive and make you look well-prepared.
Good luck.