Yes - a properly conducted opinion poll with a random sample of 1,000 people gives a 95% chance of a result that reflects the opinion of the entire US population, with a 3% margin of error.
See article from the Scientific American, below.
How can a poll of only 1,004 Americans represent 260 million people with only a 3 percent margin of error?
Also, to quote an old joke that is popular with survey researchers:
"If you don't believe in the accuracy of random sampling, next time you have a blood test, ask the doctor to take it all."