The August 27, 2010 Denver Post reports that "Two University Hospital clinics balk at government insurance".
Specifically, they are turning away patients covered by Medicare and Medicaid -- because they lose money on each one. These patients all have theoretical "coverage", but that's not the same as getting actual medical care.
Medicare and Medicaid are the government-run "universal coverage" programs for the elderly and the indigent, respectively. We can expect to hear about more such problems as the entire country moves towards a system of government "coverage".