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 a robust network of informants. If you continue to work with Mr. House, the NCR will no longer accept your help.
The NCR knows that you are working against its interests and will no longer accept your help.
The NCR has declared you a terrorist. Wherever the NCR has jurisdiction, you will be shot on sight.
If Ambassador Crocker or Colonel Moore dies, the NCR will declare you a terrorist. 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.
This quest will not fail and you may complete NCR quests if you initially trigger it with House or Yes Man's quest line and then proceed with the other one's quest line. There are two separate quests here actually (one for House and one for Yes Man), and one will not trigger if the other one is active.
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 Aaron Kimball's assassination.
Behind the scenes
"Don't Tread on the Bear!" is a reference to the Gadsden flag, a historical flag that depicted a coiled rattlesnake over the phrase "Don't Tread on Me."