You can't deny that moving excess people to various floating deadly rocks doesn't solve the overpopulation problem on Earth. The technology will evolve to get to these places over time, although getting it to affordable rates may take a lot longer.
It is likely that the birth rate would continue to drop as well, and with life expectancy extensions - in particular if women could stay fertile for longer (maybe difficult with the limited set of eggs they are born with, but I'm sure they can be kept around too) - it will likely extend even more, as people continue to stay children to older ages (both definitions of 'stay' apply here).
People would still die too, but that would move from ~70-80 years old to ~100-~120 years old on average initially. The concern is that the prolonging therapy evolves over time to be repeatable, and more effective, meaning people will live to a very very long time, and people may already be alive who will benefit from this.
I think there are strong arguments to society being stronger with new blood (to eradicate rich Trumps). So maybe forced exile to the stars once you hit a certain age is an idea. You've had a life, now continue it elsewhere building a new society from scratch, with all that experience you should have gained. And if it all goes tits up, hey, you did live a long time already, don't whine about it (not that your whines will be heard back in our solar system).
Funding mechanisms for the massive cost to society of people hanging around longer will need to be found. Fit for work doesn't mean much work will exist in the future due to automation...
That's if we're not all scrabbling for scraps in a post-Trump nuclear winter.