Joseph,
I lean towards favoring universal health coverage, but not simply because I believe the government has a “moral obligation” to provide it. Rather, the government exists to provide for the general welfare of the citizenry, and I believe increased health care coverage benefits everyone, not just the poor. Take your example of “universal coverage” by ER visits. Yes, the ER will treat everyone, even those who cannot pay, but that “model” of care is very inefficent, cost-ineffective, stresses hospitals, and delays urgently needed treatments for others. Increasing access to preventative care and clinics for non-emergency injuries and illnesses ends up being cheaper than using the ER as your primary care facility.
As far as universal housing, HUD already provides quite a few programs for low income homebuyers and renters. We can probably do it and still have the world’s largest military. BTW, taking care of health care would have the additional benefit of reducing the need for housing assistance. Health problems among earners are frequently the impetus for housing insecurity, and perhaps the majority of the chronically homeless suffer from mental health or other health problems that should be treated.