I'm just confused as to how high the Kb constant / how low the Ka constant needs to be for a base to be considered a "strong base." The conjugate base of hydrogen phosphate ion, phosphate ion, has a Kb of 2.083 * 10^-2. This number is less than 1, a number I would consider to be small. And yet phosphate ion is widely considered to be a strong base. Compared to the strong acids, which have acid dissociation constants in the billions, do strong bases require a smaller Kb?
A strong base is arguably whatever you want it to be. Ammonia seems pretty strong when it gets to your nose (its biting order comes from acting as a base), magnesium hydroxide looks powerful too when it displaces heavy metal hydroxides from solution.
For a more objective definition, Wikipedia gives the following:
Acids with a p Ka of more than about 13 [in water solution] are considered very weak, and their conjugate bases are strong bases.
This suggests that a freely soluble species with $pK_b<1$ in ambient water solution would be considered a strong base. By this criterion, phosphate ion and calcium hydroxide come up just short with $pK_b\approx2$ (the latter is limited in solubility anyway), whereas all the alkali metal hydroxides and tetramethylammonium hydroxide make it.