It's way too many people. I had four grown family members stay with me the first time and only my mom was really helping with the baby. It caused a lot of stress for me prior to their arrival (preparing for houseguests) and a lot of guilt for the two weeks after the baby was born - I couldn't leave the house and felt terrible that they were "stuck" at home with me. I ended up sending them to do sightseeing on their own.
I swore I'd never do this again until I saw the cost of a doula or night nurse - having family help you is ideal, just not a boatload of them! This time around, I'm staging visits. Only my mom (and dad) can come when baby's born to help me. Other relatives (only those who are willing to help out stay with us) can come after they leave, or several weeks after baby's born - just not everyone at the same time.
Stand firm. Just be honest and say there is no room, or that your husband needs to sleep in one room (to be able to sleep to go to work the next day) and you only have one other room for you and the baby (expect a lot of crying 24/7). Anyone who wants to help with night feedings is welcome to stay (watch many hands go down..). They may say they'll set up beds anywhere else in the house though (I'm still trying to figure out how to deal with that bit).
At the hospital, the nurses advised in the baby care class that we say the first two weeks we needed to be alone with baby to bond with her. They suggested we not tell family about the birth until afterwards (many showed up at the hospital when we asked them not to, good thing that the hospital only allowed those you wanted in for visits). They also suggested keeping a ratty old bathrobe by the entrance and throwing it on anytime there was an unexpected visitor at the door - you may not even need to act bleary and sleep deprived to shoo away folks.
Whatever you do, try to not allow them to make this into a family reunion of sorts. Been there and it's a disaster!