After Ring-A-Ding-Ding, the NCR and the Legion forgive you for any past crimes. (EDIT to clarify: This sets negative reputations back to "Neutral.") You can spend the first part of the game doing one faction's quests, totally brutalizing the other side, and then turn right around and start doing the other faction's quests -- to a point. After all, killing some folks as part of one quest locks off some other quests. You can't massacre the Legion camp for the NCR and then go back later to massacre the NCR camp for the Legion -- somebody has to be left alive to reward you.

When you get to a certain point in the main quest later in the game, you'll start to see quests listed on your Pip Boy that warn you that proceeding any further will lock off future quests with certain factions. "Don't Tread on the Bear," for instance, is a quest that appears to warn you that if you keep doing stuff with certain non-NCR factions, you're going to lose any chance to work on the NCR's main quest endings.