According to director Harold Ramis, it goes on for about 10 years (over 3,600 iterations). There are a minimum of 34 separate Groundhog Days actually depicted onscreen in the film. Ramis later corrected his earlier estimate stating,
I think the 10-year estimate is too short. It takes at least 10 years to get good at anything and, allotting for the down time and misguided years he spent, it had to be more like 30 or 40 years.
A number of factors taken into consideration include the general belief that it takes 10,000 hours to become an expert at anything (in Phil's case, regarding learning French, piano, ice sculpturing, etc.), days on screen (38), days mentioned (414) and gesture days (trying to save the old man, falling kid, etc). It could be argued that Phil learned his talents concurrently rather than consecutively, but a claim in either direction would be mere conjecture.