I'm not sure that would happen. Consider that they have an eternity to pay it back -- or really, a few hundred years given everyone will likely experience at a fatal accident on such a long timeline. What person couldn't pay back an exceedingly high price on an installment plan lasting a few hundred years?
Many countries are currently addicted to population growth. Their mentality hasn't adjusted to the rise of automation and the decline of demand for human labor. They still think we need to keep high birth rates to fund social security schemes.
What will happen in the next few decades is that fewer people will be needed to do anything really productive. More people will study and raise their kids. A smaller, richer population would be more sustainable when it comes to overfishing, overpolluting etc. We will turn the world into farms and hopefully plug all the holes that will result. Ecosystems will be much different with less variation, and humans will be trying to constantly keep the balance.
It is in this environment that we place advances in longevity.
Virtually every tech starts that way, though.
The societal upheaval of rich people getting smartphones a few years earlier is probably not something you can extrapolate to the societal upheaval from "you could live forever but you don't have enough money right now".