I know I would.
As I was reading, I saw Prim as my sister, tears grew in my eyes (seriously) and knew instinctively what I would do in that situation - exactly what Katniss did.
There is no way I would let any of my siblings go to their death (even though I wouldn't be able to do anything for my brothers), however friends are a bit tricky. I know that sounds harsh, but I don't know if I'd be willing to sacrifice myself for any of my friends, especially if my family needed me like Katniss' did.
Family is different.