Many americans are opposed to government telling them what to do. Obamacare mandates that you have health insurance - you are "fined" by way of additional tax if you can't show you have coverage (this is the way they got around the constitutional issue MsAmerican mentioned).
Some people are paying more for care since obamacare came in and are annoyed.
Some people don't want coverage because they think normal rules of health don't apply to them - I'll never be sick!! so resent paying for it or paying the tax.
The reality is we all paid for the uninsured because if you present at a hospital with an emergency, you will be treated. That cost is spread onto those insured.
The other reality is that the majority of americans would prefer obamacare to stay in place. And the majority of Trump's base are probably on medicare or medicaid and have benefited from the expansion of those programs.
The third reality is that congress has one of the best healthcare packages around.
But Trump and the republicans are off on their merry dance of illogic. It is like lords of misrule or like landing in topsy-turvy land - today we saw the republican party, the right-wing party of Law and Order, go full -on attack against the FBI and the CIA in an effort to shut down an investigation into a totalitarian, ex-communist regime's interference in our democracy. Weird times.
Oh, and I live in Massachusetts where we already had a version of obamacare - organised and instituted by our republican Governor Romney, the republican presidential candidate who ran against Obama in 08 (actually a decent man in many ways). Sometimes I think you couldn't make this shit up.