If they can get a representative sample then 1000 to 2000 is pretty good, and somewhat industry standard. Using statistical analyses on larger samples will only marginally improve quality of results. A key trick is to gain a representative enough sample, and 1000 to 2000 people tends to be enough to cover most segments/divisions of a population that are useful.

I've been reading the Foundation series by Isaac Asimov recently and its incredible how well he explained the predictability of large groups of humans. Modern statisticians are mostly a humble lot, having all been proved wrong many a time, but they all know that we can be fairly predictable on a population level. Listen to or read Nate Silver, Ben Raue, or Antony Green probably some of the most well known in our context of "Australians influenced heavily by US politics" all know they know things, but are fairly humble in their pronouncements about things, contrast this with lifestyle podcasters or most journalists and you'll see what I mean.

To put another way, a lot of statistical analysis is built off averaging and predicting those measures of central tendencies, which after a certain size is reached vary little with more size, so once you reach a fair size sample the most important, and increasingly tricky part is finding its representative. I think a famous story of this is the readers digest polls who were famously highly reliable, until circulation or readership decreased and suddenly the reliability plummeted.