I hear a lot of worries of overpopulation, but I think it's just the opposite - one of the main reasons people feel the need to have kids is because they know they're going to die some day and they want at least some part of them to continue on. Even that is sometimes not a strong enough motivation, just look at how low the population growth rate is becoming in developed countries these days. If I knew I could live forever, suddenly having kids seems a lot less important, even irrelevant.
Also, assuming this cure for aging is accomplished through technology and isn't magicked out of the clear blue sky, then all our other tech will be a lot more advanced by then too. So we'd likely be able to support orders of magnitude more people on earth, as well as ship them off to other planets.
Another possibility is that immortality is not accomplished by changing human bodies to not age, but instead through
mind uploads. In that case, resource consumption per capita would drop dramatically, and it wouldn't be a problem. Of course then you get whole new problems, like is it morally wrong to allow rich individuals to buy themselves a larger timeslice on the scheduler etc.