We use N-body simulations to study the evolution of dwarf spheroidal galaxies (dSphs) driven by galactic tides. We adopt a cosmologically motivated model where dSphs are approximated by a King model embedded within an NFW halo. We find that these NFW-embedded King models are extraordinarily resilient to tides; the stellar density profile still resembles a King model even after losing more than 99% of the stars. As tides strip the galaxy, the stellar luminosity, velocity dispersion, central surface brightness, and core radius decrease monotonically. Remarkably, we find that the evolution of these parameters is solely controlled by the total amount of mass lost from within the luminous radius. Of all parameters, the core radius is the least affected: after losing 99% of the stars, Rc decreases by just a factor of ~2. Interestingly, tides tend to make dSphs more dark matter-dominated because the tightly bound central dark matter "cusp" is more resilient to disruption than the "cored" King profile. We examine whether the extremely large mass-to-light ratios of the newly discovered ultrafaint dSphs might have been caused by tidal stripping of once-brighter systems. Although dSph tidal evolutionary tracks parallel the observed scaling relations in the luminosity-radius plane, they predict too steep a change in velocity dispersion compared with the observational estimates hitherto reported in the literature. The ultrafaint dwarfs are thus unlikely to be the tidal remnants of systems like Fornax, Draco, or Sagittarius. Despite spanning four decades in luminosity, dSphs appear to inhabit halos of comparable peak circular velocity, lending support to scenarios that envision dSphs as able to form only in halos above a certain mass threshold.