For the most part, nobody disputes that it would be a good thing if everyone in the United States had health insurance and could get health care when they needed it. This is sort of like the idea that no one would dispute that it would be better if there were fewer poor people. The conflict is not over the ends, but rather over the means. The reason that many people do not like “Obamacare” is that they do not think that it is the right way to go about making sure that people have health care.
To some degree, the controversy over Obamacare is just partisan. There are aspects of the program that people would hate much less if some other president (particularly a Repbulican) proposed them. Many conservatives simply hate Obama just as many liberals hated George W. Bush.
However, there are also serious policy reasons for people to dislike Obamacare. Mainly, people think that it is not a good idea for the government to have such a big role in providing health care. They would prefer to have a more free market approach to the issue. They feel that Obamacare would expand the power of government too much and that it would be too expensive. They feel that a free market solution to the issue would give people health care, would lower costs, and would not increase the size of the government.
So, the major conflict is not over whether it is good for people to have access to health care. The major conflict is over how to provide it to them.