1500-2000 is fine. They use random sampling and weighting. A larger sample size would decrease the margin of error but wouldn't significantly alter the results. A margin of error of +/-3.1% is fine for this kind of snapshot of public opinion.
A sample size of 1,659 out of a population size of 334,914,895, with a population proportion of 50% and confidence level of 95% gives an error margin of 2.41%.
If there's anything I would not fault somebody about, it's misunderstanding sampling in a statistical sense. Just about the biggest case of "plug into formula and pray" of all of my classes I took. I'm looking back and it's just Greek letters to me now...
Oh yes, it's not meant as a slight. It's just something that humans need to be aware of. Just like how we need a forklift to move a one-ton object, we need to run calculations and trust the math when doing statistics.