
Not urgent. A stump is a slowly decaying mass of wood, not a hazard. It is not going to fall and it poses no structural threat to a house. What it actually does is occupy the spot you probably want to replant, keep feeding decay fungi already present in the soil, and interfere with mowing. The one forward-looking concern is that some stump-colonizing root-decay fungi, Armillaria among them, can also attack living roots of nearby trees — so a stump acts as a reservoir rather than an inert object.
No danger clock whatsoever — this one can genuinely wait, and any contractor treating a stump as urgent is selling you something. Practically, a stump grinds most cheaply and cleanly while the wood is still firm; badly rotted stumps are messier and the grindings hold together poorly. If you want the spot replanted this season, that timing is the only real constraint you have.