If I put a cup over a spider, and leave it there for a day, will the spider survive?
To answer the first part of your question: it is extremely unlikely that the spider will die or be weakened after just one day.

Wolf spiders (Lycosids) are all predators. Due to variations in prey populations, and low efficiency of consumption at higher trophic levels, they are subject to inconsistent and unpredictable food supply (Greenstone and Bennett, 1980). They are very well adapted to this lifestyle and consequently, long periods of starvation often yield no behavioural changes (Persons, 1999). It is highly unlikely that the spider will die after just one day: Anderson, (1974) observed no changes in activity after starving Lycosa lenta (a species of wolf spider) for 30 days; and Tanaka and Ito, (1982) observed Pardosa astrigera (another species of wolf spider) living for up to 54 days of starvation. Age and sex of the spider are more likely to affect its behaviour and performance than food or oxygen availability (Persons, 1999).

As for oxygen consumption, Greenstone and Bennett, (1980) measure an oxygen consumption of 100µL/hr for wolf spiders. Assuming that your cup is of the size of the unit of volume of the same name, the cup (~0.237L), a small calculation (see figure) shows that there will be enough oxygen for the spider to survive for over 98 days. The oxygen concentration within the cup may decrease as it is used by the spider, however this is likely to have a minimal effect as a cup placed on a surface is unlikely to be hermetically sealed.



In short, oxygen availability is unlikely to have an effect on the spider before other limitations (such as food) are reached. However neither of these effects are likely to cause behavioural changes during the first month.

References


Anderson, J.F., 1974. Responses to Starvation in the Spiders Lycosa Lenta Hentz and Filistata Hibernalis (Hentz). Ecology, 55(3), pp.576-585.
Greenstone, M.H. &amp; Bennett, A.F., 1980. Foraging Strategy and Metabolic Rate in Spiders. Ecology, 61(5), pp.1255-1259.
Persons, M.H., 1999. Hunger effects on foraging responses to perceptual cues in immature and adult wolf spiders (Lycosidae). Animal Behaviour, 57(1), pp.81-88.
Tanaka, K. &amp; Itô, Y., 1982. Decrease in respiratory rate in a wolf spider,Pardosa astrigera (L. Koch), under starvation. Researches on Population Ecology, 24(2), pp.360-374.