There are a couple under construction. "There are now five new nuclear plants under construction in the United States (Watts Bar 2, Summer 2, Summer 3, Vogtle 3, Vogtle 4)." http://www.nei.org/Issues-Policy/New-Nuclear-Energy-Facilities/Building-New-Nuclear-Facilities
Under construction being fairly broadly defined.
The two I was thinking of were Vogtle and Grand Gulf, but I see that Grand Gulf was cancelled again a few years ago.
Actually the military has built dozens of them. Every time a sub or aircraft carrier pulls into ports and the girl/boy scouts come down for a tour, they are a few football fields away from a nuclear power plant.
Still big suckers.
http://www.westinghousenuclear.com/New-Plants/AP1000-PWR
My theory is that if nuclear power was able to progress here like in other countries the reactors and powerplants would be dozens of times more safe, several times more powerful, and about the size of a large house.