Can you become unvilified in new vegas after you become vilfied?

Answer 1

Only a few special cases let you do that - when you first exit Lucky 38 after speaking to Mr House, you'll be approached by representatives from NCR and the Legion, both wanting you to speak to their leaders. Your notoriety with their factions will be reset to Neutral if it was anything lower.

However in other cases, once you are vilified, most faction members will attack you on sight. You can do them a good deed occasionally (if you are Vilified by the Powder Gangers, you can deal peacefully with those at Vault 19) in which case your reputation with them will be upgraded to Merciful Thug, though they'll still attack on sight.