I agree with KeysMama. I want to add that if your placenta doesn't come out right away it is NOT in itself evidence that something is wrong, they just start worrying because you could be internally hemorrhaging and they wouldn't know it until you began to show symptoms of going into shock. Personally, I can tell by how I feel what is normal for me, but a midwife is on the outside and doesn't have that direct information, and is going to be getting nervous because she is ultimately (legally) responsible for your safety.
So if it were me I would sign a waiver and allow my body to do its work unencumbered. Something that helps a lot is to make sure you are warm (if you are still totally exposed after the birth, you will begin to feel the cold and will involuntarily tighten up) and squat, squat, squat. I'm one of those women who has very mild contractions after the birth, so the squatting is essential to getting the placenta out without "help". I also twiddled my nipples. Even so, mine still take at LEAST a half an hour to come naturally.
My suggestion is to not start worrying about the placenta as soon as you give birth, but rather have the midwife leave the room for a while while you sit back, snuggle into some blankets, drink some water/have something to eat, have some private time with your husband, relax, admire your baby, latch on if s/he is interested, cut the cord when it is cold and limp, hand the baby to husband, then get up and squat over a bowl and give a few soft pushes.
Betcha it works.