I am not clear on why taxpayers should not pay for the treatment of mental illness for those who are use Medicaid, Medicare, or any other government subsidized program. For one thing, the costs of not doing so are clearly greater than the costs of doing so, not simply, as the most recent tragedy demonstrates, in lost lives, but also in unemployment, crimes committed, incarcerations, and concomitantly, a far higher incidence of physical ailments. Furthermore, not addressing the problem of mental illness is a loss of whatever creativity and effort those with mental illness could give, as demonstrated so well in A Beautiful Mind (Nasar). Another troubling aspect to this stance is that diabetes, hypertension, and many other physical ailments are those we do seem to be more willing to take care of at taxpayer expense. These are incurable ailments, costing significant amounts to treat, too. I always suspect some sort of "blame" when people balk at treating the mentally ill.
I agree with the 5th post that mental illness is not just one disease, but a wide range of conditions that may fall anywhere on the continuum between pathological and normal. One consequence of tragedies such as that in Connecticut is that people seem to believe that mentally ill people are often violent. This is not the case at all, and I do believe statistics support the notion that mentally ill people are no more violent than the rest of us.
All in all, I believe it is incumbent upon a society to treat its mentally ill, for practical and compassionate reasons. It costs us monetarily, and it costs us as an ostensibly humanitarian society to not do so.