Well... I am looking at My code book right now, haha if you have one you can follow along... (you dont want one)
any size 14 awg wire rated at either 60, 75, or 90 degrees C. can work with a 20 amp circuit. Which means, the wire is rated to withstand the 20 amps that would be going through it!
However.... The code permits that if you have 14 awg wire, the overcurrent protection cannot exceed 15amps. which poses your possible problem. It will work, but it wont be to code... which, unless you have an electrical inspector coming and tearing up your walls to see what size wire you have... youre going to be fine.