I suspect it takes a clearly US liner or cruiser (or larger warship) sunk by a U-Boat with heavy loss of life... the odd garden variety merchantmen getting blown out of the water can be written off in the fog of war, but SS America or USS New York getting sunk is quite a different matter.
Add Hitler or Gobbles gloating over it and US opinion against getting involved would shift VERY rapidly. Still, suspect that puts a start more like Nov-Dec 1939 than September...
You want a way for the US to get into the war?
The US sends a BatRon consisting of the USS New York, Arkansas and Texas on a port visit to Scapa Flow at the end of the first week or so of October 1939. Being neutral, they are well lit, anchored near the entrance to separate themselves from the British combatants and do not have torpedo nets deployed.
Enter one Gunther Prien and U 47 with lots of torpedoes.
Given the low visibility, does Mr. Prien attempt to penetrate the anchorage past three high value targets, or does he look at them, yell "HELIGE SHEISS", and then set up attacks on each ship?
My guess is that later that day, October 14th, 1939 will be known as the "Day that will live in Infamy".
Belushi TD