Let's assume this fall turns into a sh*tshow because college students probably won't social distance leading to big out breaks. Let's then assume a bunch of parents pull their kids for the spring to wait out a vaccine. Let's also assume they don't have lucrative international students this year. Do most universities you all work for have cash buffers to withstand a one year shock like that? Could one year cause irreparable damage to a University? Would tuition need to increase greatly in 2021/2022 school year to make up for this?
Honestly, there's so much variance between how different systems are funded, how much they have in endowment, and how much of their budget they can cut that there isn't going to be a standard answer.
Schools with large endowments and/or strong alumni support will likely be ok. Schools that rely heavily on tuition and/or external revenue such as football could have a very rough time. R1 research institutions bring in a sizable share of their revenue from research grants, which - through the way grant cycles work won't be impacted this fall but could be deeply impacted in 2021 and beyond should there be a large retreat from state and federal grants as a result of the recession, as we saw after the great recession. And of course there's public/private, and how those are incorporated. Some public university systems are actually written into the state's constituion and so "cannot fail" (so to speak). Others get a sizable chunk of their revenue from the state coffers.
My own current state system recieves just over 30% of their operating expenses directly from the state, 59% from tuition, and the rest from "other", with an almost non-existent endowment (relative to our expenditures). We are going to be hurting. Harvard, IIRC, has an endowment large enough that it could continue to operate with absolutely no revenue for almost a decade, and that's not including their extensive non-campus real-estate holdings which could (in theory) be sold off.
As maizeman indicates, this isn't uncharted territory and most institutions have plans for budget triage which includes furloughs, canceling classes/activities etc. My university is already well into it's playbook. For obvious reasons this impacts the students, though we do what we can to still provide a quality experience. As one example, our field course spends its 3 weeks in a field station in another country is perhaps the greatest course an undergraduate who wants to become a field biologist can take -- but this year it's no travel and we are relying overwhelmingly on videos and mock data-sets. It isn't even close to being the enriching experience, nad we aren't even pretending it is.
tl;dr - the range of distress universities are in right now varies from "oh this is going to hurt a little bit" to "we are absolutely screwed if we can't charge full tuition in September". Delving into prospective institution's financials might give you some insight as to where on this spectrum a given university lies right now.
