The problem of population growth exists regardless of life extension technology. The solution we are headed for already is that a lot of people will simply starve to death.
When such issues come into discussion I always think about this island off the coast of Alaska, called St. Matthew Island:
> In 1944, 29 reindeer were introduced to the island by the United States Coast Guard to provide an emergency food source. The coast guard abandoned the island a few years later, leaving the reindeer. Subsequently, the reindeer population rose to about 6,000 by 1963[5] and then died off in the next two years to 42 animals.[6] A scientific study attributed the population crash to the limited food supply in interaction with climatic factors (the winter of 1963–64 was exceptionally severe in the region).[1] By the 1980s, the reindeer population had completely died out.[2] Environmentalists see this as an issue of overpopulation.