Challenge Level

My calculator has 26 memories - one per letter of the alphabet. When I type a sequence of letters the calculator gives the product of all the numbers in the corresponding memories. I want to put numbers in the various stores so that when I type the word ONE it returns 1, and when I type the word TWO it returns 2, and when I type the word THREE it returns 3 and so on. How far can you get ? Is there an integer above which it is impossible to get ?