200 year lifespans should not become a problem for some decades, even if we suddenly were handed them today. (We couldn't even be sure that we had 200 year lifespans until 100 years or so had elapsed.) Over the next century it is likely that productivity will increase by an unprecedented degree due to technology improvements. In that case it may be possible for only a few people, or even no people at all, to provide goods for everyone.
Even without extreme advances in productivity, if people do increase their savings (foregoing present consumption in favor of future consumption) this makes more capital available. That is, more effort goes into building machines that make machines, rather than machines that make goods. Increased capital can substitute for decreased labor, especially with improvements in technology. So this scenario also suggests that a much smaller percentage of people in the labor force will be adequate.