6000 is absolutely fine if it's a random sample of the adult population (it would be accurate to within 1%). An important thing to know is that the size of the US population doesn't affect this number.
It's much more likely that the survey has other flaws that prevented it getting a representative sample of US adults than that it got weird answers because the sample size was too small.
It's much more likely that the survey has other flaws that prevented it getting a representative sample of US adults than that it got weird answers because the sample size was too small.