14? Seven for the years with leap days and seven for the years without.
Sounds credible. A year can start with one of 7 days, and it can have either 365 or 366 days.
But I expected it to be higher :D Did we miss anything?
IF you want to get every possible date for Easter, you'll need many, many more.
You could get away with 7 if you're willing to switch calendars in the middle of the year. Buy one leap year calendar for each day of the week. If it's a leap year, use as normal. If it's not, on March 1, just switch to the calendar with the correct March 1 day.
This would be a lot easier if the year ran from March 1 to February 28/29. Which it did, for the ancient Romans - so the additional day was at the end of the year. This also explains why September through December come from roots meaning 7 through 10, despite being the ninth through twelfth months.
I would guess that around eighty is the upper bound.
Seventy should do it. Easter always falls between March 22 and April 25, a 35-day window. Once you've pinned down the day of the week of January 1 (or any other day you care about) and whether it's a leap year or not, you have five possibilities for Easter. So there are 7 * 2 * 5 = 70 possible calendars.