Here are some additional details for those of you so inclined.
Consider a simple binary choice question. This is easily modelled by the binomial distribution which has well understood distributions. (Other distrbutions may be relevant but the principles remain pretty constant across them all.) The standard deviation is given by sqrt[np(1-p)] where n is the sample size and p is the probability of the observation you are interested in (the mean is np so in what follows I will be dividing by n to talk about percentages if you are taking notes). For example, are you male? If the true p is, say, 75% then you need a sample size of approximately 833 to get a 95% confidence interval (2 s.d.) of +/- 3%.
You might also note that the closer the true p is to 50%, the larger the sample size needed. If the true p is 50% you need a sample size of approximately 1100 for the same confidence interval. Furthermore, if you want to get it within 1%, the sample size goes up dramatically - to 10,000.
The population size is pretty much irrelevant. The population matters for ensuring that your sampling is truly random, but political pollsters can use the same sample sizes in Australia (pop ~20 million) as in the US (pop ~300 million) for similar accuracy. (Sampling bias is the reason that political polls can be out by so much - if you call households during work hours you are going to get a very different sample of people than if you call at dinner time.)