They're against it because it's not a question of math, or even cost, for most Americans. There's a strong current of, "I got mine; so you get yours" in American culture. We think universal healthcare means the government digs into the pockets of responsible (aka healthy) people so it can give a free ride to the sick and lazy.
People will read this post and say, "Why should I pay 2K when I'm not even sick? That money is just being wasted on people who are gaming the system! I'm not paying for someone's diabetes medication who eats McDonald's all day! At least I know the 8K would be taking care of me and my family."
And the savings for businesses. Why should an auto business have to dedicate money and staff to coordinate healthcare? Why should school taxes have to dedicate money and staff to coordinate healthcare? And back to someone's point about private healthcare - if private healthcare is so much better, why are they afraid of the competition?
People are so against it primarily due to the primary populous of America being allergic to anything remotely Communist. It just so happens that universal/public healthcare is a socialist idea.
They don't think farther than that.
Welcome to America-where Wendy’s had to discontinue the 1/3 lb burger because Americans thought it was smaller then a 1/4 lb burger.
Sir this is a Burger King.