^Nah, it's not so bad. Say we got immortality tomorrow--the solution is to stop having kids. Now, this brings up some really thorny human rights issues, but not on the same scale as the other options you're contemplating, I think, namely genocide or mass starvation or both. The planet
can support six and change billion people. Not with current Western-average energy expenditures and eating habits, to be sure, but that too can be changed, and is indeed a historical aberration anyway ('course you could say the same thing about democracy, so that sort of reasoning could be dangerous

).
The problem would be its lack of universal applicability. Immortality would probably soon become within reach of the American/European/democratic East Asian middle classes, and perhaps the Chinese middle class as well, and of course the upper classes of all societies. However, the majority of the planet's population would not see much of a benefit, and I suspect it would be easy to wage some class warfare based on religious as well as social justifications... so that would be a downside, although it might (however messily) solve the overpopulation concern. : /
And to tackle your last point first, clearly there would have to be a huge shift toward a more socialist economic system, for the reasons you state, as well as to prevent a war against the rich that would make Krasny Oktyabr look like a hearing at an OSHA appeals board.
I do believe that it's unlikely that any society advanced enough to contemplate radical life extension technologies will not be so commensurately advanced economically as to provide a system at least as reasonably labor-free as our current one, and probably much less labor-intensive than even our own.
And hey, if I can't stay young and pretty, immortality doesn't really have much of a point.
