The NCR's biggest enemy is themselves and the game does a pretty good job of telling you why and how. If the courier doesn't solo carry the NCR and do all it's dirty work it's assumed the Mojave chapter either gets owned or will likely spread itself wayyyy too thin. The NCR makes its own enemies and there's no need for a comparable faction to resent them.

There's a list of factions that NCR oppose (Khan's, Followers, BOS, the independent towns) mainly due to NCR's aggressive expansionism however writing them in a way to band together would probabaly be ridiculous but it can be done through an independent playthrough