Some of the above posts aren't accurate--it depends on the loan. I had one private loan from my post-bac that I had to start paying because it didn't have an in-school deferment once I completed the degree it was loaned for. I tried talking with them and with my financial aid office, but unfortunately with private loans they dictate the terms. So I paid the $80/month or so. My other private loan I was able to defer through graduation.
Read your MPN--that will tell you the details. And if you do have to start repayment, just call your lender--sometimes they'll surprise you and work with you and allow you to defer (if they know you're in medical school, then they know you're almost certainly going to pay that loan in full, so it also helps them make more money the more you defer your loans). Obviously that one lender of mine wasn't very flexible, but my other loan was from Wells Fargo and they let me defer the loan even when I was a "non-degree" student (ie., my glide year when I had finished and obtained my post-bac, but was invited to TA and took one course/semester for fun. Even federal loans would've gone into repayment at that time. So you never know.
As for Federal loans, yes, they qualify for an in-school deferment. I think you could in theory defer those through old age if you were still a student...