I have a different perspective as someone that works at a university that relies on international students for the revenue they bring in. Increasing costs in higher ed are certainly a hot-button issue, but I don't think it is an exaggeration to say the situation would be cataclysmic if universities suddenly had to make up the difference. It's a much more complex issue than I think people realize. Decreased funding from states or the federal government, combined with increased spending on amenities, administrative bloat, and non-academic ventures like athletics would almost certainly mean pricing out affordable University education for many or most Americans. I would bet the vast majority faculty, staff, and students would admit fewer international students if they could. Larger class sizes, over-crowded residence and dining halls, and language and cultural barriers are things that immediately come to mind for directly affecting everyone at a university today.
Most international students have visas (F1, J1, etc) that do not permit them to work even when they are students, let alone after they finish their degrees. They typically can get a waiver to stay a few extra months after graduating, but they still need an employer sponsor, which is very rare. Some like those on J1s are even required to return to their country.
Personally, I don't see this as sustainable. Many countries like China have been dumping all kinds of money into their own Universities and have been recruiting the better Chinese scientists to return home and prop up their own higher Ed. I don't think it will happen anytime soon, but if the prestige of a US education wears off, it is going to hurt us in more ways than one.