Projections that there's enough uranium for 200 years[1] are based on levels of present utilization: around 3.7% of global energy use[2]. Bump that to 100% and we'd run through all available reserves in less than a decade (7.4 years, if you're counting).
Solar energy (including solar mediated via plants, wind, or water), hydrogen fusion, possibly geothermal energy, or with really long odds: hydrocarbon prospecting from another body (say, maybe Titan) are the only energy sources which could last a considerable human population for the possible maximum lifetime of the species.
Yes, a small Mars outpost could be powered off of nuclear power for a considerable period, but that would take away from available nuclear fuel supplies on Earth.
The likelihood of managing usable sustainable fusion under terrestrial or other contained circumstances are fairly unlikely IMO.
The fuel supply for conventional reactors is limited because they rely on U235, which is 0.7% of uranium. Fast reactors could use the rest of the uranium. That multiplies the supply by more than 100x because it means you can economically retrieve fuel from lower-grade ore, or even from seawater, which would extend the supply to millions of years. Russia has several fast reactors in production right now, and is building more.
Liquid thorium reactors are another option. There's no thorium in seawater, but on land there's several times as much thorium as U238, and it's all the same, useful isotope. China has an aggressive R&D program hoping to get a prototype reactor ready in a decade.
But personally I think it's likely that we will achieve sustainable fusion in the fairly near future.
My understanding of seawater is that uranium concentrations are 0.01 - 0.02%, and that it's not thermodynamically feasible to extract it for energy at those concentrations.
...which says that EROI is 22 assuming a conventional reactor. Ie., we'd get 22 times as much energy out as we spent on extraction. With a fast reactor the ratio would be a hundred times better, since we could use all that uranium instead of 0.7% of it.
Also, geological processes bring more uranium to the surface, and rivers are constantly putting more uranium in the oceans, at a rate that would provide 25 times our current electricity usage. If we keep our usage at that level, uranium will last until the sun goes out.
That's only proven reserves, though. Thorium right now is in basically no demand. Given the extremely high energy density of the fuel, A LOT of ores will become economically extractable.
It might not be 64ky, but >1ky seems to be very realistic.
What about regular, fission nuclear power?