Some are, most are not. At least the ones with influence.
From a humanitarian standpoint, I'd like to see everyone get good care when needed. From a personal standpoint, I have excellent coverage at minimal cost to me. So it is difficult to get the tens of thousands like me that have good care to want to change. What we need is some good information.
First is cost. You state your care is paid for by taxes. By covering everyone that has nothing right now, there will be some savings as the local hospital is charging me more to cover the ones that will not pay. What are the differences? Until I can see number, I'm not willing to pay a lot of additional taxes.
Lastly, who is covered? I'm willing to pay a little more to assist those in need, the low income family or those that cannot work due to physical or mental problems. I'm not willing to pay to cover some lazy ass that is not contributing to the system.