September 29 is the anniversary of the creation of the regular military of the United States under the Constitution, replacing the Continental Army that had taken orders from the Confederation Congress. On the final day of its very first session, the First Congress passed "An act to recognize and adapt to the Constitution of the United States, the establishment of the troops raised under the resolves of the United States in Congress assembled," officially creating a military that the president commanded. It was no coincidence that President Washington had been prodding the Congress to take this step; he wanted to be commander-in-chief of something, as specified in the new Constitution.
September 30 is the day in 1948 that Edith Roosevelt, Teddy's second wife and widow, died. Caroline Harrison, wife of Benjamin Harrison, was born on October 1, 1832. (It is also Jimmy Carter's 83rd birthday.)
On October 2, 1919, President Wilson suffered the stroke that left him incapacitated for many months. President Lincoln proclaimed Thanksgiving to be the fourth Thursday in November on October 3, 1863.
Finally, October 4 is the 50th anniversary of the launch of Sputnik I. Not a presidential day, strictly speaking, but President Eisenhower said that it was "one small ball in the air, [and] it's something which does not raise my apprehensions, not one iota." On the other hand, Lyndon Johnson, then Senate majority leader, said: "The Roman empire controlled the world because it could build roads. Later, when men moved to sea, the British Empire was dominant because it had ships. Now the communists have established a foothold in outer space. It is not very reassuring to be told that next year we will put a 'better' satellite into the air. Perhaps it will even have chrome trim and automatic windshield wipers."