Most likely if nothing had been done only minor problems would have occured, things that could be worked around and adjusted manually as long as you were aware of them, not total meltdowns. (basicly stuff they did beforehand now, correcting the system by " telling" them, no it is not actually a sunday today, but a monday, in the 21st century not the 20th)
Also, the consequences would have been bigger than something you can correct in a few minutes by just rewriting a few lines of code. A lot of automated systems work with inner clocks that, if incorrect, will mess their operations.
If you're writing one of those you know the answer, just not the exact word.
and Wikipedia recognizes it: https://en.wikipedia.org/wiki/Year_2000_problem