What do I do? Do I talk to the lieutenant? He doesn't say anything about invading.

They will invade it?
Well now I just want my bullets back!

I think they do once you finish some quests with Eddie. I can't even speak to Eddie tho.

You need to do a series of tasks for Eddie under the quest heading 'I Fought the Law'. If you can't talk to Eddie...

I'll just kill all the powder gangers.

Put on powder ganger armor and walk in the front door and start doing missions for eddie.

That's what the faction armors are for you know...

oops...Eddie is one of those people I want my bullets back from now.

Named characters can see through armor. That's why the guard at the door would become hostile when I walked through the door even after I payed 100 caps. I used a stealth boy and all the characters in Eddie's office including himself are hostile towards me.

That is what I did to talk to Eddie when I was disliked by the Powder Gangers.
I don't know if you can get away with it if you are vilified though

[EDIT] Guess not

Correct - talk to Eddie (the Powder Gangers leader) in the 2nd floor of the administrative offices (?) inside the facility, and do his quest line (http://fallout.wikia.com/wiki/I_Fought_the_Law), and he'll ask you to find out the NCR's plans to invade. Then go to Primm, and you can (apparently) talk to the locals and get the info, or more easily (which is what I did), pickpocket the plans off of the NCR LT. Then you can talk to the NCR LT and betray Eddie, and you'll be assigned to meet up with some NCR NPC near the camp and do the assault.

If the Power Gangers are hostile, well... shame on you! Use silenced weapons and sneak kills against them to prevent that... or, if it's too late for that, you can improve your rep with the Power Gangers by rescuing some of their people that got taken as slaves from Nipton. (http://fallout.wikia.com/wiki/Booted) Again, to avoid losing rep with the Legion, use a silenced weapon and kill while "[HIDDEN]" in sneak mode. If it's too late for that also... dunno... old save? New character? Console cheat?

I ended up doing the Booted quest **after** helping the NCR storm the facility (which got me from neutral to hated), and it bumped my status back up with the Powder Gangers to "Sneering Punk," so they weren't hostile to me, despite having massacred countless numbers of them. (Same trick works to keep the Legion from going hostile, while purging their slaving asses from the wasteland.)

Are you sure? I did it at disliked, I assumed you could as vilified as well.

But if not then I apologize, didn't meant to mislead you.

I just one-man-armied my way through. Didn't need the NCR.

Keep in mind there are at least 2 if not 3 side-quest relevant characters in the correctional center.

If you are vilified you can not get in to facility peacefully. Some named NPC including Eddie will see through your uniform disguise if you get too close and attack.

If you want to prevent bad reputation with faction, kill them only while sneaking/hidden. Also injuring somebody does not lower reputation, only killing. So if you have quest where you need to help somebody to fight other faction members, just try to bring health of enemies down but let them be finished by others (like quest to save Goodsprings from Powder Gangers attack).

It seem killing somebody while wearing their uniform is regarded especially vile. I got vilified immediately.

But the NCR soldiers die too and you get atleast 1k caps worth of loot from safes, powder dead bodies, and ncr dead bodies!!