That's me as well - socially quite a ways left of center, fiscally quite a ways right of center. I think universal healthcare is a wonderful idea. I also think it's batsh*t crazy to create new taxes to pay for it when we have all kinds of potential revenue sitting on the table. Tax loopholes that can be closed, inefficient government spending (I'm talking about the $200 hammer, not necessarily spending on programs I don't agree with as a whole) and the like.
The difference is in the messaging. I'm willing to bet that if you asked conservatives "Do you support the general idea that all Americans should have access to affordable healthcare?" the vast majority would say that they do. They just want to find a reasonable way to pay for it, outside of "take some more from those who have to give to those who don't". But liberals have done a fantastic job of convincing Americans that conservatives want to deny coverage to Americans. Hell, the Hillary Clinton for President 2016 Facebook page had a post about all the things the Republicans asked for (and didn't get) during the shutdown. Three of the items were "deny heathcare coverage to the president and staff, deny healthcare coverage to the cabinet and staff, deny healthcare coverage to congress and staff." Nobody wanted to deny coverage - they wanted to get rid of the government subsidy. It would seem that the liberal mindset then is that, if the government isn't providing something (or paying for a chunk of it), that thing isn't available. The government isn't giving me a subsidy to buy healthcare - they must be denying me access to healthcare as well.