Just a guess, but, it looks like models from the 50's or 60's and could have been made by the Thomas White Sewing Machine Co. I googled and found one from that era named "The White Fair Lady" but not one named "The White House" I didn't search further but might be a place to start.

This machine is indeed a Brother... I have one just like it, but instead of White House, it says Brother.

I also own this machine. Mine also says Brother on it. I have a copy of the owners manual. My recent discovery is that the big honking foot that came with it is a ruffler foot!