What you're talking about essentially exists in the form of Western Governors University. It was a project started by the Governors of the 19 western states to supply accredited online degrees to the under privileged (as a new Governor is elected to one of the member states s/he becomes a member of the board of trustees)

Read more here: http://en.wikipedia.org/wiki/Western_Governors_University

It isn't free but the cost is something like $2,000 for every 6 month period and you can take as many classes as you can handle in that time frame.