DS1307 RTC adjust drift automatically

Looks like I'll have to use a GPS receiver since sourcing the radio-based receivers appears difficult, plus I get the benefit of a GPS system, if I want it. The breakout board from adafruit appears enticing, it'll be interesting to see to what extent trimming the oscillator will work. What is the minimum time you think you need to trim with reasonable perfection? For something as accurate as the DS3231, I figured I'd need at least a month.