Rule number one of science reporting: Never take the headline at face value. NASA is not building a warp drive. NASA is building an experimental device that will help test the plausibility of a proposed theoretical way of FTL travel. Or maybe they already built it, the article is a year old.
That should be awesome enough on its own without having to coach it in terms of how NASA 'might build its first warp drive'. Sure, if this works, and all the other theoretical problems are solved, and so on and so forth.
When that theory first came out it was thought that you would need a space ship with the mass of Jupiter to use the drive, so it was considered too impractical for real life.
Now with the latest research into it the amount of energy and mass has been reduced significantly and they believe a ship as small as 1600 pounds could use the "warp-drive." Too bad that they still need some "exotic" material to make it work.
If I'm reading it right, 1600 pounds is not the mass of the
ship, rather the mass equivalent of the energy you'd need to warp spacetime in the manner required by this version of the Alcubierre drive. It's an amazing improvement over Alcubierre's original version, though still a shitload of energy (on the order of exajoules, or a significant fraction of the world's yearly energy consumption).