I'm guessing Presidents Day because it is supposed to honor both Washington and Lincoln.
This post was edited by SpunkySenior at February 19, 2018 7:10 AM MST
It is definitely not the first because the holiday applies to two presidents and the first is a single possessive. It could probably be either of the other two.
2) The story of Presidents’ Day date begins in 1800. Following President George Washington’s death in 1799, his February 22 birthday became a perennial day of remembrance. At the time, Washington was venerated as the most important figure in American history, and events like the 1832 centennial of his birth and the start of construction of the Washington Monument in 1848 were cause for national celebration.
"President's Day" would be in the vein of "Mother's Day" and "Father's Day"; a day to honor the office of president in general. In the way that Mother's Day is the day of the mother, "President's Day" is the day of the president.
"Presidents' Day" is another way of saying "the day of the presidents"; rather than emphasizing the office of president, it refers to all the presidents at once. This is, according the sources I've consulted, the more traditional name of the holiday. And it is the most frequent that I see, browsing the internet right now.
"Presidents Day" is abjuring the possessive construction all together. Here we have a situation of a noun adjunct: the noun "presidents" is modifying "day". It's not a short day or a happy day, it's a presidents day! This seems to be less common in the names of holidays. Grammatically, it's acceptable, but it is is a somewhat newer construction.