That's extremely hard to believe. Does he show the math?
But! Palo Verde has three reactors. If you assume that he really meant "reactor" rather than "plant", and went with 1 GW as its output, it would take a little more than 19 years.
[1] http://www.tsp-data-portal.org/Breakdown-of-Electricity-Gene...
[2] https://en.wikipedia.org/wiki/Palo_Verde_Nuclear_Generating_...
Wikipedia says there are about 50,000 coal plants online, as ScottBurson notes, but I know there aren't 50000*11/39 = 14000 nuclear plants in the world. Googling "number of nuclear power plants" returns an answer of 438 "reactors." Obviously the number of plants is somewhat smaller, and we don't know if the statistic includes military reactors on subs and carriers. Call it 400.
So what I've missed appears to be the fact that a typical nuclear plant must generate 14000/400 = 35x as much power as a typical coal plant. The largest plants of both types are in the gigawatt class, so most of those 50000 coal plants must be significantly smaller.
So, at some point, it must have been decided that most nuclear plants needed to be as powerful as the largest coal plants. Absent a change in policy, that clearly denies the nuclear industry the benefits of economies of scale... unless those economies are realized on a per-plant basis. (E.g., if it doesn't cost much more to build a 1 GW nuke plant than a 100 MW one, you might as well build the former.)
That's not necessarily an argument that we shouldn't build more nuclear power capacity; only that we can't expect it to be the entire solution to global warming this century.
[0] https://en.wikipedia.org/wiki/Fossil-fuel_power_station#Envi...
Capacity of large nuclear power plant unit: ~1 GWe [1] Total world electricity consumption is 20,900 TWh/year [2], of which 40% is generated by coal power plants. A total power of ~1000 GWe, so you'll need 1000 nuclear power plants to replace all coal-fired plants by nuclear power plants.
[1] https://en.wikipedia.org/wiki/List_of_nuclear_power_stations [2] https://en.wikipedia.org/wiki/Electric_energy_consumption
At the same time, it does not prove that it's impossible to go mostly nuclear. It just shows the need for mass production of smaller reactors, so that we can make&install them by thousands a month across the globe.
1. https://en.wikipedia.org/wiki/World_energy_consumption
2. https://en.wikipedia.org/wiki/List_of_nuclear_reactors#Russi...