I researched this on my own almost three years ago and posted it in a few threads.
How late is too late
That was actually incorrect information that even I believed. It was that way for about a month after 9/11 and that was it. I also 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 manifest must be submitted to Homeland Security one hour before sailing. It was 24 hours a few months ago.
The current booking requirements are:
Carnival: Day of sailing
RCI: 24 hours before sailing