It is quite possible "deadline" has two separate origins. There's the unquestioned Civil War usage, but the phrase dropped out of use for 50 years before showing up again as the time a newspaper had to be "dead" in order for the presses to start printing it.
So in both cases, it's a line (literal or figurative) you can't cross without horrible consequences, but it isn't clear the first usage led to the second one.