I can't remember the exact place I saw the poll but I believe it was Sports Illustrated's 50 States profiles. At the end of their 50 states run I believe they tallied the numbers of those surveyed with a similar question of what's your favorite sport or something to that effect. I seem to remember that the WNBA finished tied with the NHL and the NBA was ahead.
However, the one thing to keep in mind about polls is that the numbers can be schewed to make any result. Its much like political polls, you can say do you believe x is better than y and get one result but you can also change the wording slightly do you believe x is doing a better job than y and get a different result.
I put no stock in polls really, the better testament to which league or sport is more popular is to take a combination of attendance (as a percentage of capacity as MLB and NFL stadiums are much larger than NHL and NBA arenas), merchandise sales and tv ratings. Since I am no math wizard, I am not sure what formula you would use to come to a reasonable figure to stack one against the other. But those are a truer test of how well liked one league or sport is over another.
Out of curiosity of the 4 major leagues (NFL, NBA, NHL and MLB) how to they rank in your mind in terms of your own enjoyment?
For me I'd say:
1. NHL
2. MLB
3. NFL
4. NBA
However, I'd rank alot more things above the NBA, but for statistical purposes I will leave those 4. For the purpose of this experiment I will use the 4-3-2-1 point method. Obviously, the NHL will win as this is a hockey board but it would be interesting to see which is 2-4.