Due to the principle of special relativity, if you could build a spaceship that accelerates at a constant 1g, the people on the ship could get anywhere in the entire galaxy without aging more than 24 years [1]. So a person could easily travel from one end of the galaxy and back in a normal human lifespan. Of course to a "stationary" observer (e.g. on Earth) watching the spaceship, it would appear to take a couple hundred thousand years for the trip to take place. But this doesn't matter a bit to people aboard the ship (well, aside from the fact that everyone they left behind on Earth would be dead just a few months into their trip).
So the hard part isn't getting people to live long enough. It's building a ship that can accelerate at a constant 1g for years on end. :)
[1] https://en.wikipedia.org/wiki/Space_travel_using_constant_ac...
Immortality -- to me at least -- doesn't seem like it will end up providing that many benefits to humanity as a whole. Population control will become much more difficult, unless all over-aged males are somehow forced to undergo a vasectomy. And I highly doubt that people living longer will lead to increased productivity. On the contrary, I think that people will rely on welfare more and more as they age, not because of health, but because of burnout. The obvious solution to this is the creation of a general AI that provides the majority of humans with unlimited income for life. But then, if everyone is rich, people will quickly get bored after experiencing everything they're interested in, making immortality essentially useless!
Even if it's the case, we're also doing steady progress in the "make people more robust" department: orthopedics, transplants, pacemakers, better nutrition and supplements, better environmental health, ...
I guess it makes sense, because there's strong and continuous economic pressure to achieve those things, while there isn't a case (yet?) for getting to hibernation via baby steps.
Says you.