The exact contents of this quest vary per your actions. It can result in one of five outcomes:
The NCR has a robust network of informants. If you continue to work with Mr. House, the NCR will no longer accept your help.
The NCR has a robust network of informants. If you continue to work with Yes Man, the NCR will no longer accept your help.
Little escapes the eyes of NCR Rangers. If you continue to work with Caesar's Legion, the NCR will brand you a terrorist.
The NCR has declared you a terrorist. Wherever the NCR has jurisdiction, you will be shot on sight.
The NCR knows that you are working against its interests and will no longer accept your help.
The first three actions are, obviously, the result of aiding an opposing faction. The fourth is a result of gaining general NCR infamy, usually through killing their troops. In the case of opposing faction quests, it will first activate as a warning upon the completion of a certain quest in the series. Completing another quest will fail the mission. You will no longer be able to take on NCR quests once this happens, and any NCR quests active will immediately fail, as well. In the latter two cases, the entire faction will be hostile to you and NCR rangers will be sent to kill you.
Failing this quest will cause Ambassador Crocker and Colonel Moore to disappear from the game world, to reinforce the idea the player is no longer able to continue down the NCR quest line.
Your reputation with the NCR will not be lowered if you complete this quest via House or Yes Man. In fact, so long as you have done nothing else to antagonize them, it is possible to breach the El Dorado Substation and get them to agree to a truce with the Brotherhood of Steel (in Yes Man's path) without dropping your reputation below Idolized. They will even still accept your help in preventing President Kimball's assassination.
If you exit the Lucky 38 for the first time and have the unnamed NCR trooper approach you, but you fast travel before you initiate conversation, he will follow you until he tells you Ambassador Crocker wishes to talk to you. This can lead to problems if you enter Nellis Air Force Base and let him catch up to you. If the trooper catches up to you and talks to you, as he walks out of Nellis, the Artillery Barrage will annihilate him. This will result in failing "Don't Tread on the Bear!" and may result in you being labeled as a terrorist.