What if these "random" people just by coincidence happen to favor one party or another? Wouldn’t these polls then be considered inaccurate? If that is the case then why have a poll given the risk of inaccurate information? Why poll 1,000 people in a country of 30,000,000?
Because they work. If done well, they are highly accurate. Political campaign ads are based on the same kind of polling data, so politicians who say they do not believe in polls, or use them, are living because they use the same methods and techniques almost daily.
Look at all the advertising based on data mining and marketing analysis. If you could not predict how large numbers of people will behave based on a sample of that population there would be no such thing as advertisements and commercials because they would not be effective. However, we are surrounded by it because it works. It works so well in fact, that companies like amazon.com will not even reveal how many mathematicians they employ, let alone what they are working on.
Sampling is a complex issue itself and there are different methods and strategies that can be applied depending on the information you want to gather.