I forgot to mention: The "flat insurance" model (Kopfpauschalen-Modell), as envisaged by the CDU, does not include those who are privately insured. It sticks to the dual system of private and public health insurance. The monthly contribution will still be one for the public system. For privately insured people, the CDU-model would not change anything. But for publicly insured people, those who are paying less now (because they are earning less) would face rising contributions while those paying (and earning) more would benefit. Some amelioration for the jobless and the poor is supposed to be tax-financed. (This is the main point of critique from a market-liberal point of view like from the FDP.)

But this whole Kopfpauschalen-model is not only about contributions. It also means changing health insurance from an allocation-financed system into a capital-covered system. But this seems to be too far-leading at the moment.

By the way: 88 % of all Germans are publicly health-insured.

Look here for for further information.