Load bearing wall and basement beam don’t line up. Want to add a header and larger opening. Problem?
Without seeing any pictures its hard know so they would help. If its a 60's ranch house I would think that the roof is a truss roof and the roof load is on the outside walls. With that said there would be no load bearing walls interior. The purpose for the beam running down through the center of the basement is for floor support because back in the 60's truss roofs were becoming popular but not truss floors, they used 2x6/2x8/2x10 depending on the span and placed them on a steel W beam in the center. 
Its all guesses without images - but go in your attic to see what type of roof you have, you have to look up before you look down in the basement.