Four presidents have birthdays in February: George Washington ( February 22), William Henry Harrison (February 9), Abraham Lincoln (February 12), and Ronald Reagan (February 6). To recall why observers hold Washington and Lincoln in such high regard, consider Washington's Farewell Address and Lincoln's Second Inaugural Address.

Washington's Birthday
In terms of Federal law, there is no “President’s Day”—it’s Washington’s Birthday!

Lincoln issued an 1862 proclamation declaring February 22 a day of celebration of the “birth of the Father of his Country.” This is the earliest document in The American Presidency Project collection to mention Washington's Birthday.

A February 22 Federal holiday was created in law passed in 1879. The following is from the Revised Statutes Forty-Fifth Congress.  Note that the actual language of the statute does not refer to Washington, but the reference of the date would have been clear to all.  The law was extended to cover all Federal employees, not just those in Washington, DC, in 1885.[1]

In 1968 a law on uniform public holidays was passed, taking effect in 1971, to place almost all Federal holidays on Mondays, creating three-day weekends.  That law explicitly named “Washington’s Birthday”—there was no mention of Lincoln. (See complete text reproduced below.)  By the terms of that act, Washington’s Birthday would always be observed on the 3^rd Monday in February.
 
As is described further below, such a reform had been under discussion since the 1930s.

What about Lincoln?

Lincoln's Birthday, February 12, was separately commemorated by many presidents starting with Hoover. 

In several Messages on President’s Day, President Clinton emphasized that he understood the holiday to honor both Washington and Lincoln.  While this combined observance is not a feature of Federal law, it is, however, true in law in many states.

According to the website officeholidays.com, nine states[2] observe only Washington’s Birthday, and nine more[3] observe no holiday on the 3^rd Monday.  Arkansas combines Washington’s Birthday and “Daisy Gatson Bates Day.”[4]  The remaining 31 observe President’s Day (or "Presidents’ Day") or some explicit combination of Washington and Lincoln Birthdays.

President’s?  Presidents’?  Presidents?

There’s a pretty big difference in meaning depending on where you put the apostrophe!  Again according to officeholiddays.com, by far the most common spelling in state law is “President’s.” In the American Presidency Project’s documents directly involving a president’s speech or message (the “Presidential” document category), the most common spelling ( N=12) is “President’s.” Second is “Presidents’” (s' N=7).  A distant third (N=1) is “Presidents” (no apostrophe).  The use of "President's" suggests the day is honoring a specific president (or two, perhaps), while "Presidents'" would suggest honoring all Presidents together.

Uniform Public Holiday Act

In 1951, a trade association called the National Association of Travel Organizations (NATO) introduced draft legislation they called Model Uniform Monday Holiday Legislation. NATO promoted this in both the state and the national legislatures.  By one account (Knight, 1971) the drive to switch "non-religious" holidays to Monday can be traced as far back as 1937.  NATO advocated placing most national holidays on Mondays so as to generate three-day-weekends.  They, and their allies, saw a vast array of benefits to individual travelers, business, and government in reducing the number of disruptive mid-week holidays.The NATO representative did not argue, in 1967 testimony before a Senate committee, for renaming Washington's Birthday as "President's Day."  But that had been a feature of their proposals reported in major newspapers in the mid-1950s.  In 1967-68 many others did support using the holiday to honor both Lincoln and Washington or to honor all presidents.  (In the Senate hearings, spelling of the proposed holiday name broke down as follows:  Presidents:  31;  Presidents': 31;  President's: 16.)

The 1967 holiday reform process began with 18 bills on Monday holidays.  Of those, nine proposed retaining "Washington's Birthday" but observing it on the third Monday of February.  Seven more proposed also to change the name to "President's Day."  Writing in 1971, Leavitt Knight observed that "it was openly stated in Congress that not all Presidents were held in the same esteem as George Washington." (Knight, 1971 )

The sponsor of the legislation that eventually passed, Florida Senator George Smathers, stated in Senate Hearings that his preference was that "Washington's Birthday would be changed to Presidents' Day, to honor not only our first President but all of our Presidents." 

In the 1967-68 debates, Tennessee Rep. Dan Kuykendall offered this keen prediction:  "If we do this, ten years from now our schoolchildren will not know what February 22 means.  They will not know or care when George Washington was born.  They will know that in the middle of February they will have a 3-day weekend for some reason.  This will come."

Text of the Uniform Monday Holiday Act