1000 is enough for this case.
Depends on how "accurate" you want to measure a ratio. Here the ratio is the percentage of Americans that support net neutrality.
In this case, sample size is 1000, estimated ratio is 76%, the 95% confidence interval is 76% +/- 2.65%, which means if you repeat this survey again, you have a 95% chance that new estimated ratio is within 76% +/- 2.65%.
Edit: 99% confidence interval is 76% +/- 3.48%