If you can get a good rep with the ncr you get emergency radio. Using it gives you a ncr ranger or trooper. That usually helps at low levels. Since the ranger or trooper will draw there attention you will be able to run away. Another option is right when you notice them coming and haven't attacked yet use a stealth boy if you have one. Also if you can run as fast as you can to the nearest settlement. They will go away when you reach a crowded area and will leave you alone. In my experiences they don't find you right away after doing this. So you'll be good for a bit but always come back when your like yay I'm almost there.
Then I don't know where you are at in the game but it sounds like your in nipton saving those powder gangers and are probably on your way to novac or vegas. If so I have noticed staying off of the main roads help a bit but not much. Also if you can go back to the legion camp and take their armor and wear it. As long as you wear the armor you will stay at neutral and no assassins come and try to kill you but right when you take it off they will be after you again. Also if you do get some legion armor make sure to take it off near ncr bases.
I was actually finishing Novac. And heading to boulder city when they decided to attack on the long stretch of road.
I ran all the way to boulder sitting pumping stimpak into me, med-x, mentats, etc. Whatever could keep me alive. Using up my doctor bag so I can continue running my ass. I ended up in boulder city with everything crippled.