I think there's some lead time involved before federal agencies can furlough employees. (30 days?)
Of course, every department will be motivated to concentrate the impact as much as possible on critical (e.g., ATC), sympathetic (vaccines for kids), or public-facing (TSA checkpoints, but not check baggage screening) services to make the cuts seem terrible/draconian. TSA's case may be unique because they are uniquely hated and the public, though probably not the media, may be more inclined to blame Pistole/Nappy instead of Congressional Republicans for problems at airports. So *maybe* TSA will behave and just cut down on standing around, pointless gate screenings, etc.
My understanding is that these "cuts" still keep us at or above 2006 spending levels, and really are cuts in growth not cuts in spending. So if everybody were being honest, things would get not worse than they were in 2006. In a family of real people with real jobs who pay real taxes, a "pay cut" means your pay went down in absolute dollars (not inflation adjusted). In the government, a "cut" means you didn't get as much of a raise as you wanted.