Would there be any problem to the overall plan if I have the basement contractor pour a few small footers in the concrete floor of the basement for posts to support a beam going down the center of the basement ceiling. The basement portion of the house is going to be 20x44. I would probably go with 2x10's for the floor rafters.
No problem at all, that is the way its done. Review chapter 4 and 5 in the building code for sizes and spans.