I don't know of anyone who thought the world itself would end. Many, including myself, thought there would be tremendous problems, up to and including societal collapse, UNLESS the problems were fixed. Fortunately, most important problems were fixed in advance, so there was not much disruption to speak of.
However, were it not for the warnings being heeded, who knows what would have happened. I worked at a large aerospace company at the time (!999), and the IT people were running around in a tizzy fixing and testing for months prior to the clock turning over.