There are four types of consonants:
Those that use the vocal cords: -- m,n,l
Those that use only air:
sibilants -- s, sh
fricatives -- f, ph
plosives -- b,p,k,t,d
It is possible to sing using m, n and l, but is impossible with the rest, since they last only a fraction of a second and since they are the result of a distinct movement of the tongue and lips, they cannot be 'held' to keep the sound going - they need they vocal folds to be able to produce a prolonged sound.