A thousand voters is actually a perfectly good statistical sampling for the US population.
What matters is that
the daily Mail isn't overly credible
they don't mention how the thousand voters were selected.
A thousand people is enough to get you into single digit margin of error for a population the size of the US. If you find them by dialing random landlines, or mailing surveys to people with a voter history, your sample biases towards the demographic that still has landlines or that's willing to take the time to fill out a paper survey.
A 100,000 person response rate for a snap poll is basically impossible. Not enough people say yes to taking political polls. Most polling is done with 1000-1500, and if you want higher response rates, you have to look at aggregators like 538.