Sorry, but maybe it comes from the business term, "in the red"? :(
ANSWER:
Good question. I came across this on a sports blog:
"There isn't an official explanation from the NCAA or NFL on why the area from the 20 yard-line to the end zone is commonly referred to as the red zone. However, as the majority of the scoring takes place from inside the 20 yard-line, it is believed that the term came about because it is the hottest area of scoring on the field, and generates the most action. Sorry there wasn't a stranger or more exciting explanation. "
http://blogs.eveningsun.com/latter/qa/
Rugby sometimes uses the same term for the area inside the 22-meter line, so it could be that football borrowed it from rugby (as it did with many other terms).
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i remember hearing it for the first time around 2005. It was started by a television production company. They needed to give that "20 yard to td" a name so they could later create a channel that would show all and only redzone plays and charge you money for it.