It cannot be stated too many times that extended life will not produce overpopulation or the sorts of resource shortages constantly feared by Malthusians. Even if it did, that would be a prompt to solve both the resource problem and the aging problem, not a prompt to condemn billions to death by relinquishing the clear path ahead to widespread, cheap rejuvenation treatments. Malthusian visions of any form are simply incorrect, however. They are based on a static view of the world in which the nature of resources doesn't change. Humans, however, are ingenious and motivated by the prospect of future scarcity and increased prices to develop new resources and new technologies. This has happened over and again, yet for some reason we still have Malthusians. There is some flaw in human nature that makes it hard to see that the world is being changed for the better even while we are in the midst of radical progress in science and technology.
A classic objection to the radical extension of life is: "But such an extension will lead to an overpopulation crisis!" We think this is important to refute that idea that longevity equates to overpopulation, because it is not a harmless idea. Actually, this formula is so widespread that it is used to stop investment of public money in longevity research, because people making decisions have serious reserves: nobody wants to invest money in a project that would lead to an overpopulation crisis! Therefore, it is important to avoid turning longevity into a scapegoat. In addition, if we knew how to live much longer in good health, it would not be very humane to force people to die at 80 in order to avoid some hypothetical overpopulation problems.
The fertility rate is the average number of children per woman in a given population. When this rate is around 2, the population is considered stable. Being overly concerned about life extension, while easily accepting a fertility rate slightly greater than 2, is simply not rational. Even if death disappears tomorrow morning, the resulting population increase would be smaller than the one observed during the baby boom. And should it happen in Sweden, then after 50 years, the population increase would only be 30%, which is within the limits of the population increases observed during the last century. Therefore, even after such an unlikely event (and assuming that it is a problem), we should have more than enough time to adapt. But we are far from being at this point: living 50 more years would already be a major scientific advance! There is no good reason to ban or to refuse to finance longevity research.
Last but not least, keep in mind that the context can radically change before life expectancy increases significantly. This has already been the case during the industrial revolution. We could discover new ways to provide shelter and food to more people at a smaller price, make new zones habitable, and even, in the long-term, colonize new planets. It is evident that a radical increase in population is not a "goal" in itself. But, assuming that it happens, it's consequences may be far less dramatic than what we imagine today, because the context will have evolved. In the previous century, some people thought that London would eventually be entirely covered with horse manure. Today, this idea makes people laugh! In past predictions, we always underestimated the increase of life expectancy and always overestimated population growth. Are we not making the same mistake again? Two centuries ago, Malthus (the most famous thinker of overpopulation) was making apocalyptic predictions based on the scale of one century. Today, the population has been multiplied by 8 and instead of collapsing, the standards of life have significantly increased.