ROCK6, if a sample is truly random, you don't need much over 2 or 3 thousand to be very accurate, like within 2 or 3 percentage points. With 1000 respondents, the margin of error is probably closer to 5%, but still not large. The sample size is not the issue.
It's how the question is asked. I worked in market research, and I could get any answer I wanted if I just asked the question the right way. I guarantee the question was something like "do you support background checks for gun purchases and closing loop holes that allow criminals to purchase guns without background checks." Who wouldn't answer yes to that?