To construct a king quilt you don't necessarily need a king sized space. You may want space to lay out your quilt while you assemble all of your blocks into the quilt top, but you need very little sewing space to actually sew it together. You may need more space to quilt it, depending on how you do it.
It seems you are asking about hand quilting frames here. I don't hand quilt, but someone else should be able to help.
Putting together your workspace will depend on how much space you have to work with, what you need to do in the space, and how much equipment/fabric/gadgetry you have to store. The smaller your space, the more each station will need to pull double or triple duty. If you had to, you could press, cut, and sew on the same smallish surface. Quilting on a frame, whether by hand or machine, requires another allotment of space. Can you give us some details about what you are working with?