Even the premise, why would people want immortality, in what form they'd want it (like an eternal youth solution would be more appealing, which would depend on the technology), would they really want it, could their mind even handle that much longevity, or their motivation to remain alive could stay with them.
Now that's a curious thought. In a world where death doesn't exist, would people be motivated to do anything really? Greatest motivation behind all human activity is the fear of death (even procreation, or simply sex is motivated by this ultimately).