If I massacre NCR troopers until I'm vilified, what will I be unable to do? Will they attack me on sight, or will I have to be declared a terrorist for that to happen?

They'll attack you on site and you won't get to complete a lot of missions.

Also, in my experience, sometimes being vilified also means they'll attack you even if you're dressed the faction's clothing - they just take a little longer to recognise you.

They will also send out hit squads when you are out exploring.

Lt. Boyd's witty comments.