Looking at it in the long term, his conclusion is inevitable. We have about one to two billion years to get off this planet, and out of this star system. The sun has about another four or five billion years to run, but in just over a billion years, it will get brighter, which will make it hotter here on this planet. Although this is not a universal opinion, the disagreement is simply and only about the time-line, which is why I said one to two billion years.
This page at Universe Today explains the likely life span of the sun.
Sagan got his doctorate in planetology, and he was, from high school onward, an exceptional student. This is basic astrophysics--stars get old, and then they "die" in a rather spectacular manner. They go out with a bang, not a whimper. In the case of our star, it will swell into a red giant (engulfing the earth), before collapsing into a white dwarf. So, his statement is absolutely accurate. Any civilization, anywhere, eventually has to leave its star system. If it doesn't, it's doomed.
