One of the lower moments in recent Unitarian Universalist history was when a few years ago Massachusetts Blue Cross/Blue Shield dropped the UUA's group plan. By that point it had gotten rather expensive and the few that remained -- so I heard; I could be wrong -- were those higher-needs persons who could not be insured elsewhere. For years, until last fall, there was no Association-wide insurance plan.
But even now, given the cost of premiums through that program and others, I suspect there are many ministers and church staffers without health insurance. I had none from when I graduated seminary to when I came to Washington: three years. I think I'm still paying for a 1998 emergency room trip -- which consisted of a shot of steroids and a wide-spectrum antibiotic -- for a case of strep throat. And we know that this problem affects many, many people. Ms. Theologian and her husband have high-deductible plans which looks to me like being at risk, since actually procuring medical services is very costly. I'm fortunate enough to have enrolled in a relatively low-cost (and low-service) HMO for the tenure of my unemployment. (I might have gone on Hubby's fully-paid work plan but seeing as we cannot be legally married, the value of the insurance becomes taxable income; his taxes and the cost of the HMO plan were about the same, so I decided to take the HMO since I would be able to administer it more easily.) But if I was older or lived in another city, this would not have been a viable option.
We can talk about the health system's brokenness. We can talk about taking care of ourselves through changed behaviors. We can (and ought to) talk about church-based health care, like Parish Nursing. But in the mean time, we need to help those without access to aid or insurance develop some financial "street fighting" skills: negotiate a price, seek outside help, make and keep a payment plan.
I found the discussion at Metafilter ("44 million+ uninsured people in America") very helpful and practical.