The building = The Pentagon.
From a NYT article titled "Cuts Give Obama Path to Create Leaner Military."
[T]here may be an opening to argue for deep reductions in programs long in President Obama’s sights, and long resisted by Congress....The programs Obama has long longed to reduce are listed as: nuclear weapons, the military medical insurance, and next-generation warplanes (like the F-35).
[I]nside the Pentagon, even some senior officers are saying that the reductions, if done smartly, could easily exceed those mandated by sequestration, as the cuts are called, and leave room for the areas where the administration believes more money will be required.
These include building drones, developing offensive and defensive cyberweapons and focusing on Special Operations forces.
ADDED: The corresponding article in The Washington Post is "F-35’s ability to evade budget cuts illustrates challenge of paring defense spending":
With an ear-ringing roar, the matte-gray fighter jet streaked down Runway 12 and sliced into a cloudless afternoon sky over the Florida Panhandle. To those watching on the ground, the sleek, bat-winged fuselage soon shrank into a speck, and then nothing at all, as Marine Capt. Brendan Walsh arced northward in America’s newest warplane, the F-35 Lightning II.It streaked and sliced and — they must be thinking — if only it would shrink into nothing at all.
When the F-35 finishes testing, “there will be no yes-or-no, up-or-down decision point,” said Pierre Sprey, who was a chief architect of the Air Force’s F-16 Fighting Falcon. “That’s totally deliberate. It was all in the name of ensuring it couldn’t be canceled.”When... but we're not there yet.