It's mentioned a few times in the game, and also you can read on various sites----the Legion far outnumbers the NCR. By a lot. The Legion has sheer numbers on their side, not to mention many of them are completely insane. If the courier had died, then no doubt the Legion would take the dam, unless Mr. House stopped pitting them against each other and backed the NCR.
No way, man, I don't do signatures.