It is under your deck because the deck is dry, dark and close to food, and in most cases it will not stay long. Adult opossums are among the few mammals that keep no permanent home. They move between temporary dens, which include tree hollows, logs, abandoned burrows, sewers and buildings, and they den alone. A lone opossum that appeared under your deck this week is often somewhere else next week, which is why a "wait and watch" plan is reasonable for a single adult in mild weather, as long as the gap gets closed once it leaves.
Two situations change the timeline. The first is a mother with young. Opossums in our region breed twice a year, from January through late March and again from mid May into early July. A litter averages 6 to 9 babies, each the size of a honeybee at birth. They attach inside the pouch and nurse for 60 to 65 days, leave the pouch at about 70 days but keep riding on her back, and are independent at roughly 100 days. A female who has chosen your deck as the nursery will use it for the better part of two to three months, and she will defend it. On Long Island that means a den found in March or April, or in July and August, should be assumed to hold young until proven otherwise.
The second is cold. Opossums do not hibernate, but when temperatures fall to the mid teens or low 20s they stop moving and stay in a den for several days at a stretch, and groups of up to eight will share one winter den for warmth. A December opossum under your deck may be there through every cold spell until March, and it may not be alone.
So the honest answer is: days, if it is one adult in mild weather; months, if it is a nursery or a winter den. The visible clues that tip it toward months are nesting material being dragged in, the same animal coming and going nightly for more than a week, and the season.