@ Everyone complaining about sample sizes:
What Queen is trying to get across is that the size of the US population doesn't even enter the equations for this kind of thing*. It might just as well be infinite.
Imagine that instead of asking people how they believe about armed rebellion, we were flipping a biased coin, with some probability p of landing heads. Further, imagine that after flipping it 863 times, we had observed that 251 times we got heads. We perform some calculations, approximate some things by Gaussian distributions, and come up with an estimation for the actual value of p, of about 0.29 with a margin of error of 3.4%
Now, suppose someone comes along and says "Huh? How can you possible obtain any meaningful result by flipping the coin less than a thousand times? Why, you could continue to flip that coin for years and years and years, getting billions of results! Surely that number is completely meaningless"
That is what comparing the sample size to the size of the US population is. If you think you cannot obtain meaningful results because the upper limit of the number of experiments you can perform is really big, then you are essentially arguing that the entire field of statistics is useless. Which, y'know, if you wanna do that, it's your deal.
I'm not defending the study, for all I know maybe they had a terrible protocol for determining who they call that skewed the results, or the questions were asked in a weird way, or whatever. There is plenty of ways this could be bad statistics. But the margin of error they derived from their sample size is not. Not by much, anyway, I haven't actually sat down and done the math, but since 3% is around 1000, 3.4% for 863 is probably not that far off.
*It does matter somewhat, if you perform the exactly correct probability calculation. Not if you do statistics.