A perfect example of this is shown in the chart above. It is taken from a recent CNN/Opinion Research Poll (taken between November 18th and 20th of 843 nationwide adults, with a margin of error of 3.5 points). When asked if they favored Obamacare, about 58% said they did not and only 40% said they did. If that was all that was reported (and it is all most media outlets are reporting), then it might give the impression that most Americans would favor repealing Obamacare. But that is just not true. A majority of Americans do not want it repealed.
Fortunately in this poll, CNN delved a bit deeper. They asked the question again in a slightly different way -- asking those who opposed Obamacare to state why they opposed it. And those results looked quite different (as shown in the chart below).
I am in that 14%. If asked whether I favored Obamacare, I would probably say no. I think a single-payer system (something like Medicare for everyone) would be much better -- because it takes profit out of the insurance coverage (reducing cost), puts medical decisions back in the hands of doctors, and covers everyone with insurance. But if I was asked whether Obamacare should be repealed, I would say absolutely not! Obamacare did solve a few problems (and half a loaf is better than no loaf at all). We need to go forward, not backward, in fixing our health care system (and I believe that most, if not all, of the 14% would agree with that).
And a couple of other questions in the poll (shown in charts below) also tend to show that most Americans have not given up on Obamacare, and aren't ready to repeal it. When asked if Obamacare was a failure, most Americans (53%) said it was too soon to tell, and 8% said it was already a success. That's 61% who aren't ready to give up on Obamacare. In addition, a majority (54%) say they believe the problems being experienced by Obamacare right now will be solved.