"An analysis of the United States National Health Care Act by Physicians for a National Health Program estimated the savings at $350 billion per year in 2008. Others have estimated a 40% savings due to elimination of insurance company overhead costs." -
http://en.wikipedia.org/wiki/Single-payer_health_care
And read the many references in the footnotes.
Whats more a non-profit government system is far fairer- paying claims according to administrative law while profit-insurance companies do everything they can to avoid paying claims in order to maximize profits.
. . . . .