You need a CPL to be a CFI (this is US terminology; a UK "CFI" is just a self appointed title for the bloke who runs the flying school) and a CPL/IR to be a CFII.
As mentioned, you don't need an ATP to instruct but I wonder if perhaps you need one to instruct or sign somebody off for an ATP checkride?
A US ATP is relatively achievable. The Euros screwed their up with the 500hr multi crew requirement (which is totally out of a private pilot's reach financially; well maybe Elton John could do it) but in the USA you can get a single engine ATP in a C150. (Won't be of any use done in a C150, with no TP/jet type ratings, but you get the idea). You need the 1500/100 hrs TT which many private pilots have, and the ATP is still only 1 written exam. The real work of the ATP is of course in the type rating(s) which is where it should be.