You can use the cruise line's website, another site that was mentioned before, other online sites or use a good travel agent to book last minute.
I too believed that it was 72 hours before sailing until I contacted the cruise line and found out the correct answer.
I was always perplexed why some cruise sites and even the cruise lines displayed cruises that were sailing one or two days later.
It was 72 hours for about a month after 9/11 and that was it. I believed, who I thought was a "reliable" source, that it was 72 hours but have now learned I need to verify things on my own.
The Homeland Security requires that the manifest must be submitted one hour before sailing.
The current requirements for "booking" the cruise are:
Carnival Corporation: Day of sailing but before submission of manifest.
RCI: 24 hours before sailing