I don't know if this is new or not but I found a way to gain easy Legion fame while I was playing.
You must have an explosive skill of at least 50. Head to Cottonwood Cove and Speak with Decanus Severus. Choose the dialogue option "DO YOU SEE MUCH ACTION AGAINST THE NCR?" then choose "THAT IS ALL FOR NOW" then choose "I CAN SHOW YOU HOW TO DISARM THE NCR'S MINES" With an explosive skill of 50 or above you can show him how to disarm a mine. Repeat this to gain fame with Caesar's Legion. This will not affect your relationship with the NCR.
NOTE: This will not work with the patch and it will not work if you are vilified from Caesar's legion.
Another good place is Nelson I believe giving the guy dog tags and this isn't a glitch. That doesn't hurt it either although you actually have to find them. If you go down in the little cavern area between Camp Forlorn Hope and Nelson they get into fights with each other constantly I've observed and there are always a couple NCR guys that get killed that have the tags on them you can take for this. Come back later and they should be at it again and you could find more. Not as efficient obviously, but a real easy way to bump it up without having to do any quests.