Jokes going to be on you, and probably the people who thought they were kidding by making this request, if the white house pulls out a real death star made from nanorobotics and AGI they developed in secret. While it can be argued this stuff is far off, it really can't be argued that it's impossible. Short version of nanorobotics is this: You make one nanobot (atomically precise robot the size of a blood cell with manipulator arms for moving atoms), it can then make a second, those two can make four, those four can make eight and so on. Being a million times smaller than human scale machines, they would move a million times faster, so you'd end up with trillions or more in a day, more than enough. Nanobots could make vast structures of atomic precision, controlled by massive amounts of nanocomputer based AI.
Building a death star would be as easy as ordering a happy meal. Along with things like eternal life spans (heat death, big crunch, etc. permitting), no diseases, no aging, omnipresent crime prevention, etc. I doubt anyone would actually build a death star if they could, except to say 'gee, look at this cool thing I built' but certainly not impossible.